This is SpectralSequences.info, produced by Macaulay2, version 1.25.11

SpectralSequences -- a package for working with filtered complexes and spectral sequences
*****************************************************************************************

Description
===========

Spectral sequences, although notoriously technical, are very useful in
applications---especially when they degenerate quickly. By contrast, little is
known about their general structure when they fail to degenerate quickly.  Even
in cases when the terms in the spectral sequences are well understood, the maps
remain mysterious. One of the motivations behind this package is to shed light
on spectral sequences through examples.  Its purpose is to allow for effective
calculations of particular kinds of spectral sequences. As one general
situation, which illustrates some capabilities of this package, let k be a
computable field, S a k-algebra of finite type, C a bounded chain complex of
finitely generated S-modules, and FC a bounded ascending filtration of C.  This
package is capable of computing, under these assumptions, the spectral
sequence---especially the differentials on each page---determined by FC.

Constructors used in this package
=================================

  * How to make filtered complexes from chain complex maps
  * Filtrations and tensor product complexes
  * Filtrations and homomorphism complexes
  * Filtered complexes and simplicial complexes
  * I-adic filtrations of chain complexes and their spectral sequences

Other examples which illustrate this package
============================================

  * Computing the Serre Spectral Sequence associated to a Hopf Fibration
  * Balancing Tor
  * Spectral sequences and hypercohomology calculations
  * Spectral sequences and connecting morphisms
  * Spectral sequences and non-Koszul syzygies
  * A spectral sequence which fails to degenerate quickly
  * Seeing Cancellations
  * Edge homomorphisms
  * Examples of change of rings Spectral Sequences

More easy topological examples
==============================

  * Identifying anti-podal points of the two sphere
  * The fibration of the Klein Bottle over the sphere with fibers the sphere
  * The trivial fibration over the sphere with fibers the sphere

Authors
=======

  * David Berlekamp (see http://www.math.berkeley.edu/~daffyd )
    <daffyd@math.berkeley.edu>
  * Adam Boocher (see http://www.math.utah.edu/~boocher )
    <boocher@math.utah.edu>
  * Nathan Grieve (see http://www.math.unb.ca/~ngrieve ) <n.grieve@unb.ca>
  * Eloisa Grifo (see http://people.virginia.edu/~er2eq/ )
    <eloisa.grifo@virginia.edu>
  * Gregory G. Smith (see http://www.mast.queensu.ca/~ggsmith )
    <ggsmith@mast.queensu.ca>
  * Thanh Vu (see http://math.berkeley.edu/~thanh ) <vqthanh@math.berkeley.edu>

Version
=======

This documentation describes version 1.0 of SpectralSequences, released 20
September 2016.

Citation
========

If you have used this package in your research, please cite it as follows:

+-----------------------------------------------------------------------------+
|@misc{SpectralSequencesSource,                                               |
|  title = {{SpectralSequences: A \emph{Macaulay2} package. Version~1.0}},    |
|  author = {David Berlekamp and Adam Boocher and Nathan Grieve and Eloisa    |
|  howpublished = {A \emph{Macaulay2} package available at                    |
|    \url{https://github.com/Macaulay2/M2/tree/stable/M2/Macaulay2/packages   |
|}                                                                            |
|-----------------------------------------------------------------------------|
|Grifo and Gregory G. Smith and Thanh Vu},                                    |
|                                                                             |
|}}                                                                           |
+-----------------------------------------------------------------------------+

Exports
=======

  * Types
      * FilteredComplex -- the type of all filtered
        complexes
      * Page -- the type of all pages
      * PageMap -- the type of all page maps
      * SpectralSequence -- the type of all spectral
        sequences
      * SpectralSequencePage -- the type of all
        spectral sequence pages
      * SpectralSequencePageMap -- the type of
        all spectral sequence page maps
  * Functions and commands
      * associatedGradedHomologyObject,
        -- compute the associated graded homology object
      * connectingMorphism -- use spectral sequences
        to compute connecting morphisms
      * edgeComplex -- the edge homomorphisms
      * filteredComplex -- make a filtered complex
      * filteredHomologyObject -- compute the
        filtered homology object
      * homologyIsomorphism -- compute the homology
        isomorphism
      * netPage -- display a small portion of a given Spectral
        Sequence page
      * page
      * pruningMaps -- compute the pruning maps on a
        spectral sequence page
      * spectralSequence -- construct a spectral
        sequence
      * spectralSequencePage -- construct a
        spectral sequence page from a filtered complex
      * spectralSequencePageMap -- compute the
        maps on a spectral sequence page
      * spots -- which spots does the given page has a module.
  * Methods
      * "associatedGradedHomologyObject(ZZ,ZZ,FilteredComplex)" -- see
        associatedGradedHomologyObject, --
        compute the associated graded homology object
      * basis(List,SpectralSequencePage)
        -- generators of a particular
        degree
      * "basis(ZZ,SpectralSequencePage)" -- see
        basis(List,SpectralSequencePage),
        -- generators of a particular
        degree
      * ChainComplex ** FilteredComplex
        -- filtered tensor product of complexes
      * "FilteredComplex ** ChainComplex" -- see ChainComplex ** FilteredComplex,
        -- filtered
        tensor product of complexes
      * chainComplex(FilteredComplex),
        -- the ambient chain complex of a filtered complex
      * chainComplex(SpectralSequence)
        -- the underlying chain complex of
        a Spectral Sequence
      * connectingMorphism(ChainComplexMap,ZZ)
        -- use spectral sequences
        to compute connecting morphisms
      * degree(Page)
      * describe(Page) -- real description
      * describe(PageMap) -- real description
      * describe(SpectralSequence), --
        real description
      * describe(SpectralSequencePage)
        -- real description
      * describe(SpectralSequencePageMap)
        -- real description
      * "edgeComplex(SpectralSequence)" -- see edgeComplex,
        -- the edge homomorphisms
      * expression(SpectralSequence)
      * "FilteredComplex ^ InfiniteNumber" -- see FilteredComplex ^ ZZ,
        -- the filtered pieces
      * FilteredComplex ^ ZZ -- the filtered
        pieces
      * "FilteredComplex _ InfiniteNumber" -- see FilteredComplex _ ZZ,
        -- the filtered pieces
      * FilteredComplex _ ZZ -- the filtered
        pieces
      * filteredComplex(ChainComplex),
        -- obtain a filtered complex from a chain complex
      * filteredComplex(Ideal,ChainComplex,ZZ)
        -- I-adic filtrations
        of chain complexes
      * filteredComplex(List) -- obtain a
        filtered complex from a list of chain complex maps or a nested list of
        simplicial complexes
      * filteredComplex(SpectralSequence)
        -- obtain the filtered complex
        associated to the spectral sequence
      * filteredHomologyObject(ZZ,ZZ,FilteredComplex)
        -- compute the
        filtered homology object
      * hilbertPolynomial(SpectralSequencePage)
        -- the Hilbert polynomial
        of a spectral sequence page
      * "Hom(ChainComplex,FilteredComplex)" -- see
        Hom(FilteredComplex,ChainComplex),
        -- the filtered Hom complex
      * Hom(FilteredComplex,ChainComplex)
        -- the filtered Hom complex
      * homologyIsomorphism(SpectralSequence,ZZ,ZZ,ZZ)
        -- the
        homology isomorphism
      * inducedMap(FilteredComplex,ZZ)
        -- the i th inclusion map in a
        filtered complex
      * max(FilteredComplex) -- maximum spot
        where the given filtered complex has a module.
      * min(FilteredComplex) -- minimum spot
        where the given filtered complex has a module.
      * minimalPresentation(SpectralSequence)
        -- a minimal presentation of
        a spectral sequence
      * "prune(SpectralSequence)" -- see
        minimalPresentation(SpectralSequence),
        -- a minimal presentation of
        a spectral sequence
      * minimalPresentation(SpectralSequencePage)
        -- a minimal
        presentation of a spectral sequence page
      * "prune(SpectralSequencePage)" -- see
        minimalPresentation(SpectralSequencePage),
        -- a minimal
        presentation of a spectral sequence page
      * net(FilteredComplex)
      * net(Page)
      * net(PageMap)
      * net(SpectralSequence)
      * net(SpectralSequencePage)
      * "netPage(Page,List,List)" -- see netPage, -- display a
        small portion of a given Spectral Sequence page
      * new Page
      * "page(List,List,Page)" -- see page,
      * Page _ List
      * page(SpectralSequencePage)
      * PageMap _ List
      * pruningMaps(SpectralSequencePage)
        -- compute the pruning maps on a
        spectral sequence page
      * ring(Page)
      * SpectralSequence ^ InfiniteNumber
        -- the infinity page of a spectral sequence
      * "SpectralSequence _ InfiniteNumber" -- see SpectralSequence ^ InfiniteNumber,
        -- the infinity page
        of a spectral sequence
      * SpectralSequence ^ ZZ -- the kth page of
        a spectral sequence
      * SpectralSequence _ ZZ -- the kth page
        of a spectral sequence
      * spectralSequence(FilteredComplex)
        -- construct a spectral sequence
        from a filtered complex
      * SpectralSequencePage ^ List -- the
        module in the i,j position on the page
      * SpectralSequencePage _ List, --
        the module in the i,j position on the page
      * spectralSequencePage(FilteredComplex,ZZ)
        -- construct a spectral
        sequence page from a filtered complex
      * "spectralSequencePageMap(FilteredComplex,ZZ)" -- see
        spectralSequencePageMap, -- compute the maps
        on a spectral sequence page
      * SpectralSequencePageMap ^ List,
        -- the p,q th map on of a spectral sequence page
      * SpectralSequencePageMap _ List,
        -- The p,q th map on of a spectral sequence page
      * "spots(Page)" -- see spots, -- which spots does the given
        page has a module.
      * spots(ChainComplex) -- which spots does
        the given chain complex has a module.
      * spots(FilteredComplex) -- which
        spots does the given filtered complex has a module.
      * spots(PageMap)
      * support(ChainComplex) -- nonzero
        parts of a chain complex
      * support(FilteredComplex)
      * support(Page) -- which non-zero modules
        appear in the given page.
      * support(PageMap)
      * support(SpectralSequencePage)
      * tensor(RingMap,ChainComplex),
        -- tensor product of a chain complex by a ring map
      * truncate(ChainComplex,ZZ), --
        compute the hard truncation of a chain complex
  * Symbols
      * pageMap
      * ReducedHomology -- name for an optional
        argument
      * Shift -- name for an optional argument
      * sourcePruningMap
      * targetPruningMap

For the programmer
==================

The object SpectralSequences, is a package (Macaulay2Doc),
defined in SpectralSequences.m2.

-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:1153:0.

A spectral sequence which fails to degenerate quickly
*****************************************************

The following example is taken from p. 127, Fig 7.2 of Zomorodian's Topology
for computing.  In that figure, a filtration of a suitable simplicial complex
is pictured.  Here we compute the associated spectral sequence. As we will see
below, the spectral sequences has nonzero maps on higher page numbers.

+-----------------------------------------------------------------------------+
|i1 : A = ZZ [s,t,u,v,w] ;                                                    |
+-----------------------------------------------------------------------------+
|i2 : D0 = simplicialComplex {s} ;                                            |
+-----------------------------------------------------------------------------+
|i3 : D1 = simplicialComplex {s,t} ;                                          |
+-----------------------------------------------------------------------------+
|i4 : D2 = simplicialComplex {s,t,u} ;                                        |
+-----------------------------------------------------------------------------+
|i5 : D3 = simplicialComplex {s*t, u} ;                                       |
+-----------------------------------------------------------------------------+
|i6 : D4 = simplicialComplex {s*t, u, v} ;                                    |
+-----------------------------------------------------------------------------+
|i7 : D5 = simplicialComplex {s*t, u, v, w} ;                                 |
+-----------------------------------------------------------------------------+
|i8 : D6 = simplicialComplex {s*t, s*w ,u, v} ;                               |
+-----------------------------------------------------------------------------+
|i9 : D7 = simplicialComplex {s*t, s*w ,t * w, u, v} ;                        |
+-----------------------------------------------------------------------------+
|i10 : D8 = simplicialComplex {s*t, s*w ,t * w, u * v} ;                      |
+-----------------------------------------------------------------------------+
|i11 : D9 = simplicialComplex {s*t, s*w ,t * w, u * v, s * v} ;               |
+-----------------------------------------------------------------------------+
|i12 : D10 = simplicialComplex {s*t, s*w ,t * w, u * v, s * v, s*u} ;         |
+-----------------------------------------------------------------------------+
|i13 : D11 = simplicialComplex {s*t, s*w ,t * w, u * v, s * v, s*u, u * w} ;  |
+-----------------------------------------------------------------------------+
|i14 : D12 = simplicialComplex {s*t, s*w ,t * w, u * v, s * v, s*u, u * w, t* |
|-----------------------------------------------------------------------------|
|u} ;                                                                         |
+-----------------------------------------------------------------------------+
|i15 : D13 = simplicialComplex {s*t, s*w ,t * w, u * v, s * v, s*u, u * w, t* |
|-----------------------------------------------------------------------------|
|u, t*u*w} ;                                                                  |
+-----------------------------------------------------------------------------+
|i16 : D14 = simplicialComplex {s*t, s*w ,t * w, u * v, s * v, s*u, u * w, t* |
|-----------------------------------------------------------------------------|
|u, t*u*w, s*u*w} ;                                                           |
+-----------------------------------------------------------------------------+
|i17 : D15 = simplicialComplex {s*t, s*w ,t * w, u * v, s * v, s*u, u * w, t* |
|-----------------------------------------------------------------------------|
|u, t*u*w, s*u*w,s*t*u} ;                                                     |
+-----------------------------------------------------------------------------+
|i18 : D16 = simplicialComplex {s*t, s*w ,t * w, u * v, s * v, s*u, u * w, t* |
|-----------------------------------------------------------------------------|
|u, t*u*w, s*u*w,s*t*u, s*u*v} ;                                              |
+-----------------------------------------------------------------------------+
|i19 : D17 = simplicialComplex {s*t, s*w ,t * w, u * v, s * v, s*u, u * w, t* |
|-----------------------------------------------------------------------------|
|u, t*u*w, s*u*w,s*t*u, s*u*v, s*t*w} ;                                       |
+-----------------------------------------------------------------------------+
|i20 : L = reverse {D0, D1, D2, D3, D4, D5, D6, D7, D8, D9, D10, D11, D12,    |
|-----------------------------------------------------------------------------|
|D13, D14, D15, D16, D17} ;                                                   |
+-----------------------------------------------------------------------------+
|i21 : K = filteredComplex (L, ReducedHomology => false) ;                    |
+-----------------------------------------------------------------------------+
|i22 : E = prune spectralSequence K ;                                         |
+-----------------------------------------------------------------------------+
|i23 : E^0                                                                    |
|                                                                             |
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |  1     |        |        |        |        |        |        |       |
|o23 = |ZZ      |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, 0}  |{1, 0}  |{2, 0}  |{3, 0}  |{4, 0}  |{5, 0}  |{6, 0}  |{7, 0} |
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |        |  1     |        |        |        |        |        |       |
|      |0       |ZZ      |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -1} |{1, -1} |{2, -1} |{3, -1} |{4, -1} |{5, -1} |{6, -1} |{7, -1}|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |        |        |  1     |  1     |        |        |        |       |
|      |0       |0       |ZZ      |ZZ      |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -2} |{1, -2} |{2, -2} |{3, -2} |{4, -2} |{5, -2} |{6, -2} |{7, -2}|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -3} |{1, -3} |{2, -3} |{3, -3} |{4, -3} |{5, -3} |{6, -3} |{7, -3}|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |        |        |        |        |  1     |        |        |       |
|      |0       |0       |0       |0       |ZZ      |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -4} |{1, -4} |{2, -4} |{3, -4} |{4, -4} |{5, -4} |{6, -4} |{7, -4}|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |        |        |        |        |        |  1     |  1     |       |
|      |0       |0       |0       |0       |0       |ZZ      |ZZ      |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -5} |{1, -5} |{2, -5} |{3, -5} |{4, -5} |{5, -5} |{6, -5} |{7, -5}|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |        |        |        |        |        |        |        |  1    |
|      |0       |0       |0       |0       |0       |0       |0       |ZZ     |
|      |        |        |        |        |        |        |        |       |
|      |{0, -6} |{1, -6} |{2, -6} |{3, -6} |{4, -6} |{5, -6} |{6, -6} |{7, -6}|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |        |        |        |        |        |        |        |       |
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -7} |{1, -7} |{2, -7} |{3, -7} |{4, -7} |{5, -7} |{6, -7} |{7, -7}|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |        |        |        |        |        |        |        |       |
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -8} |{1, -8} |{2, -8} |{3, -8} |{4, -8} |{5, -8} |{6, -8} |{7, -8}|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |        |        |        |        |        |        |        |       |
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -9} |{1, -9} |{2, -9} |{3, -9} |{4, -9} |{5, -9} |{6, -9} |{7, -9}|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |        |        |        |        |        |        |        |       |
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -10}|{1, -10}|{2, -10}|{3, -10}|{4, -10}|{5, -10}|{6, -10}|{7, -10|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |        |        |        |        |        |        |        |       |
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -11}|{1, -11}|{2, -11}|{3, -11}|{4, -11}|{5, -11}|{6, -11}|{7, -11|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |        |        |        |        |        |        |        |       |
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -12}|{1, -12}|{2, -12}|{3, -12}|{4, -12}|{5, -12}|{6, -12}|{7, -12|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |        |        |        |        |        |        |        |       |
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -13}|{1, -13}|{2, -13}|{3, -13}|{4, -13}|{5, -13}|{6, -13}|{7, -13|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |        |        |        |        |        |        |        |       |
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -14}|{1, -14}|{2, -14}|{3, -14}|{4, -14}|{5, -14}|{6, -14}|{7, -14|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |        |        |        |        |        |        |        |       |
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -15}|{1, -15}|{2, -15}|{3, -15}|{4, -15}|{5, -15}|{6, -15}|{7, -15|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|                                                                             |
|o23 : SpectralSequencePage                                                   |
|-----------------------------------------------------------------------------|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |        |        |         |         |         |         |         |       |
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
| |{8, 0}  |{9, 0}  |{10, 0}  |{11, 0}  |{12, 0}  |{13, 0}  |{14, 0}  |{15, 0}|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |        |        |         |         |         |         |         |       |
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
| |{8, -1} |{9, -1} |{10, -1} |{11, -1} |{12, -1} |{13, -1} |{14, -1} |{15, -1|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |        |        |         |         |         |         |         |       |
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
| |{8, -2} |{9, -2} |{10, -2} |{11, -2} |{12, -2} |{13, -2} |{14, -2} |{15, -2|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
| |{8, -3} |{9, -3} |{10, -3} |{11, -3} |{12, -3} |{13, -3} |{14, -3} |{15, -3|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |        |        |         |         |         |         |         |       |
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
| |{8, -4} |{9, -4} |{10, -4} |{11, -4} |{12, -4} |{13, -4} |{14, -4} |{15, -4|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |        |        |         |         |         |         |         |       |
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
| |{8, -5} |{9, -5} |{10, -5} |{11, -5} |{12, -5} |{13, -5} |{14, -5} |{15, -5|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |        |        |         |         |         |         |         |       |
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
| |{8, -6} |{9, -6} |{10, -6} |{11, -6} |{12, -6} |{13, -6} |{14, -6} |{15, -6|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |  1     |        |         |         |         |         |         |       |
| |ZZ      |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
| |{8, -7} |{9, -7} |{10, -7} |{11, -7} |{12, -7} |{13, -7} |{14, -7} |{15, -7|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |        |  1     |         |         |         |         |         |       |
| |0       |ZZ      |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
| |{8, -8} |{9, -8} |{10, -8} |{11, -8} |{12, -8} |{13, -8} |{14, -8} |{15, -8|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |        |        |  1      |         |         |         |         |       |
| |0       |0       |ZZ       |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
| |{8, -9} |{9, -9} |{10, -9} |{11, -9} |{12, -9} |{13, -9} |{14, -9} |{15, -9|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |        |        |         |  1      |         |         |         |       |
| |0       |0       |0        |ZZ       |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
|}|{8, -10}|{9, -10}|{10, -10}|{11, -10}|{12, -10}|{13, -10}|{14, -10}|{15, -1|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |        |        |         |         |  1      |  1      |         |       |
| |0       |0       |0        |0        |ZZ       |ZZ       |0        |0      |
| |        |        |         |         |         |         |         |       |
|}|{8, -11}|{9, -11}|{10, -11}|{11, -11}|{12, -11}|{13, -11}|{14, -11}|{15, -1|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |        |        |         |         |         |         |  1      |       |
| |0       |0       |0        |0        |0        |0        |ZZ       |0      |
| |        |        |         |         |         |         |         |       |
|}|{8, -12}|{9, -12}|{10, -12}|{11, -12}|{12, -12}|{13, -12}|{14, -12}|{15, -1|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |        |        |         |         |         |         |         |  1    |
| |0       |0       |0        |0        |0        |0        |0        |ZZ     |
| |        |        |         |         |         |         |         |       |
|}|{8, -13}|{9, -13}|{10, -13}|{11, -13}|{12, -13}|{13, -13}|{14, -13}|{15, -1|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |        |        |         |         |         |         |         |       |
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
|}|{8, -14}|{9, -14}|{10, -14}|{11, -14}|{12, -14}|{13, -14}|{14, -14}|{15, -1|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |        |        |         |         |         |         |         |       |
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
|}|{8, -15}|{9, -15}|{10, -15}|{11, -15}|{12, -15}|{13, -15}|{14, -15}|{15, -1|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
|-----------------------------------------------------------------------------|
|--+---------+---------+                                                      |
|  |         |         |                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|  |{16, 0}  |{17, 0}  |                                                      |
|--+---------+---------+                                                      |
|  |         |         |                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|} |{16, -1} |{17, -1} |                                                      |
|--+---------+---------+                                                      |
|  |         |         |                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|} |{16, -2} |{17, -2} |                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|} |{16, -3} |{17, -3} |                                                      |
|--+---------+---------+                                                      |
|  |         |         |                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|} |{16, -4} |{17, -4} |                                                      |
|--+---------+---------+                                                      |
|  |         |         |                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|} |{16, -5} |{17, -5} |                                                      |
|--+---------+---------+                                                      |
|  |         |         |                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|} |{16, -6} |{17, -6} |                                                      |
|--+---------+---------+                                                      |
|  |         |         |                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|} |{16, -7} |{17, -7} |                                                      |
|--+---------+---------+                                                      |
|  |         |         |                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|} |{16, -8} |{17, -8} |                                                      |
|--+---------+---------+                                                      |
|  |         |         |                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|} |{16, -9} |{17, -9} |                                                      |
|--+---------+---------+                                                      |
|  |         |         |                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|0}|{16, -10}|{17, -10}|                                                      |
|--+---------+---------+                                                      |
|  |         |         |                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|1}|{16, -11}|{17, -11}|                                                      |
|--+---------+---------+                                                      |
|  |         |         |                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|2}|{16, -12}|{17, -12}|                                                      |
|--+---------+---------+                                                      |
|  |         |         |                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|3}|{16, -13}|{17, -13}|                                                      |
|--+---------+---------+                                                      |
|  |  1      |         |                                                      |
|  |ZZ       |0        |                                                      |
|  |         |         |                                                      |
|4}|{16, -14}|{17, -14}|                                                      |
|--+---------+---------+                                                      |
|  |         |  1      |                                                      |
|  |0        |ZZ       |                                                      |
|  |         |         |                                                      |
|5}|{16, -15}|{17, -15}|                                                      |
|--+---------+---------+                                                      |
+-----------------------------------------------------------------------------+
|i24 : E^1 .dd                                                                |
|                                                                             |
|o24 = {10, -11} : 0 <----- 0 : {11, -11}                                     |
|                       0                                                     |
|                                                                             |
|                             1                                               |
|      {10, -10} : 0 <----- ZZ  : {11, -10}                                   |
|                       0                                                     |
|                                                                             |
|                   1                                                         |
|      {10, -9} : ZZ  <----- 0 : {11, -9}                                     |
|                        0                                                    |
|                                                                             |
|      {9, -11} : 0 <----- 0 : {10, -11}                                      |
|                      0                                                      |
|                                                                             |
|      {9, -10} : 0 <----- 0 : {10, -10}                                      |
|                      0                                                      |
|                                                                             |
|                           1                                                 |
|      {9, -9} : 0 <----- ZZ  : {10, -9}                                      |
|                     0                                                       |
|                                                                             |
|                  1                                                          |
|      {9, -8} : ZZ  <----- 0 : {10, -8}                                      |
|                       0                                                     |
|                                                                             |
|      {8, -10} : 0 <----- 0 : {9, -10}                                       |
|                      0                                                      |
|                                                                             |
|      {8, -9} : 0 <----- 0 : {9, -9}                                         |
|                     0                                                       |
|                                                                             |
|                           1                                                 |
|      {8, -8} : 0 <----- ZZ  : {9, -8}                                       |
|                     0                                                       |
|                                                                             |
|                  1                                                          |
|      {8, -7} : ZZ  <----- 0 : {9, -7}                                       |
|                       0                                                     |
|                                                                             |
|      {7, -9} : 0 <----- 0 : {8, -9}                                         |
|                     0                                                       |
|                                                                             |
|      {7, -8} : 0 <----- 0 : {8, -8}                                         |
|                     0                                                       |
|                                                                             |
|                           1                                                 |
|      {7, -7} : 0 <----- ZZ  : {8, -7}                                       |
|                     0                                                       |
|                                                                             |
|                  1                                                          |
|      {7, -6} : ZZ  <----- 0 : {8, -6}                                       |
|                       0                                                     |
|                                                                             |
|      {6, -8} : 0 <----- 0 : {7, -8}                                         |
|                     0                                                       |
|                                                                             |
|      {6, -7} : 0 <----- 0 : {7, -7}                                         |
|                     0                                                       |
|                                                                             |
|                           1                                                 |
|      {6, -6} : 0 <----- ZZ  : {7, -6}                                       |
|                     0                                                       |
|                                                                             |
|                  1                                                          |
|      {6, -5} : ZZ  <----- 0 : {7, -5}                                       |
|                       0                                                     |
|                                                                             |
|      {5, -7} : 0 <----- 0 : {6, -7}                                         |
|                     0                                                       |
|                                                                             |
|      {5, -6} : 0 <----- 0 : {6, -6}                                         |
|                     0                                                       |
|                                                                             |
|                  1               1                                          |
|      {5, -5} : ZZ  <---------- ZZ  : {6, -5}                                |
|                       | -1 |                                                |
|                                                                             |
|      {5, -4} : 0 <----- 0 : {6, -4}                                         |
|                     0                                                       |
|                                                                             |
|      {4, -6} : 0 <----- 0 : {5, -6}                                         |
|                     0                                                       |
|                                                                             |
|                           1                                                 |
|      {4, -5} : 0 <----- ZZ  : {5, -5}                                       |
|                     0                                                       |
|                                                                             |
|                  1                                                          |
|      {4, -4} : ZZ  <----- 0 : {5, -4}                                       |
|                       0                                                     |
|                                                                             |
|      {4, -3} : 0 <----- 0 : {5, -3}                                         |
|                     0                                                       |
|                                                                             |
|      {3, -5} : 0 <----- 0 : {4, -5}                                         |
|                     0                                                       |
|                                                                             |
|                           1                                                 |
|      {3, -4} : 0 <----- ZZ  : {4, -4}                                       |
|                     0                                                       |
|                                                                             |
|      {3, -3} : 0 <----- 0 : {4, -3}                                         |
|                     0                                                       |
|                                                                             |
|                  1                                                          |
|      {3, -2} : ZZ  <----- 0 : {4, -2}                                       |
|                       0                                                     |
|                                                                             |
|      {2, -4} : 0 <----- 0 : {3, -4}                                         |
|                     0                                                       |
|                                                                             |
|      {2, -3} : 0 <----- 0 : {3, -3}                                         |
|                     0                                                       |
|                                                                             |
|                  1          1                                               |
|      {2, -2} : ZZ  <----- ZZ  : {3, -2}                                     |
|                       0                                                     |
|                                                                             |
|      {2, -1} : 0 <----- 0 : {3, -1}                                         |
|                     0                                                       |
|                                                                             |
|      {1, -3} : 0 <----- 0 : {2, -3}                                         |
|                     0                                                       |
|                                                                             |
|                           1                                                 |
|      {1, -2} : 0 <----- ZZ  : {2, -2}                                       |
|                     0                                                       |
|                                                                             |
|                  1                                                          |
|      {1, -1} : ZZ  <----- 0 : {2, -1}                                       |
|                       0                                                     |
|                                                                             |
|      {1, 0} : 0 <----- 0 : {2, 0}                                           |
|                    0                                                        |
|                                                                             |
|      {16, -18} : 0 <----- 0 : {17, -18}                                     |
|                       0                                                     |
|                                                                             |
|      {0, -2} : 0 <----- 0 : {1, -2}                                         |
|                     0                                                       |
|                                                                             |
|      {16, -17} : 0 <----- 0 : {17, -17}                                     |
|                       0                                                     |
|                                                                             |
|                           1                                                 |
|      {0, -1} : 0 <----- ZZ  : {1, -1}                                       |
|                     0                                                       |
|                                                                             |
|      {16, -16} : 0 <----- 0 : {17, -16}                                     |
|                       0                                                     |
|                                                                             |
|                 1                                                           |
|      {0, 0} : ZZ  <----- 0 : {1, 0}                                         |
|                      0                                                      |
|                                                                             |
|                             1                                               |
|      {16, -15} : 0 <----- ZZ  : {17, -15}                                   |
|                       0                                                     |
|                                                                             |
|      {0, 1} : 0 <----- 0 : {1, 1}                                           |
|                    0                                                        |
|                                                                             |
|      {15, -17} : 0 <----- 0 : {16, -17}                                     |
|                       0                                                     |
|                                                                             |
|      {-1, -1} : 0 <----- 0 : {0, -1}                                        |
|                      0                                                      |
|                                                                             |
|      {15, -16} : 0 <----- 0 : {16, -16}                                     |
|                       0                                                     |
|                                                                             |
|                           1                                                 |
|      {-1, 0} : 0 <----- ZZ  : {0, 0}                                        |
|                     0                                                       |
|                                                                             |
|      {15, -15} : 0 <----- 0 : {16, -15}                                     |
|                       0                                                     |
|                                                                             |
|      {-1, 1} : 0 <----- 0 : {0, 1}                                          |
|                     0                                                       |
|                                                                             |
|                             1                                               |
|      {15, -14} : 0 <----- ZZ  : {16, -14}                                   |
|                       0                                                     |
|                                                                             |
|      {-1, 2} : 0 <----- 0 : {0, 2}                                          |
|                     0                                                       |
|                                                                             |
|      {14, -16} : 0 <----- 0 : {15, -16}                                     |
|                       0                                                     |
|                                                                             |
|      {-2, 0} : 0 <----- 0 : {-1, 0}                                         |
|                     0                                                       |
|                                                                             |
|      {14, -15} : 0 <----- 0 : {15, -15}                                     |
|                       0                                                     |
|                                                                             |
|      {-2, 1} : 0 <----- 0 : {-1, 1}                                         |
|                     0                                                       |
|                                                                             |
|      {14, -14} : 0 <----- 0 : {15, -14}                                     |
|                       0                                                     |
|                                                                             |
|      {-2, 2} : 0 <----- 0 : {-1, 2}                                         |
|                     0                                                       |
|                                                                             |
|                             1                                               |
|      {14, -13} : 0 <----- ZZ  : {15, -13}                                   |
|                       0                                                     |
|                                                                             |
|      {-2, 3} : 0 <----- 0 : {-1, 3}                                         |
|                     0                                                       |
|                                                                             |
|      {13, -15} : 0 <----- 0 : {14, -15}                                     |
|                       0                                                     |
|                                                                             |
|      {13, -14} : 0 <----- 0 : {14, -14}                                     |
|                       0                                                     |
|                                                                             |
|      {13, -13} : 0 <----- 0 : {14, -13}                                     |
|                       0                                                     |
|                                                                             |
|                             1                                               |
|      {13, -12} : 0 <----- ZZ  : {14, -12}                                   |
|                       0                                                     |
|                                                                             |
|      {12, -14} : 0 <----- 0 : {13, -14}                                     |
|                       0                                                     |
|                                                                             |
|      {12, -13} : 0 <----- 0 : {13, -13}                                     |
|                       0                                                     |
|                                                                             |
|      {12, -12} : 0 <----- 0 : {13, -12}                                     |
|                       0                                                     |
|                                                                             |
|                    1               1                                        |
|      {12, -11} : ZZ  <---------- ZZ  : {13, -11}                            |
|                         | -1 |                                              |
|                                                                             |
|      {11, -13} : 0 <----- 0 : {12, -13}                                     |
|                       0                                                     |
|                                                                             |
|      {11, -12} : 0 <----- 0 : {12, -12}                                     |
|                       0                                                     |
|                                                                             |
|                             1                                               |
|      {11, -11} : 0 <----- ZZ  : {12, -11}                                   |
|                       0                                                     |
|                                                                             |
|                    1                                                        |
|      {11, -10} : ZZ  <----- 0 : {12, -10}                                   |
|                         0                                                   |
|                                                                             |
|      {10, -12} : 0 <----- 0 : {11, -12}                                     |
|                       0                                                     |
|                                                                             |
|o24 : SpectralSequencePageMap                                                |
+-----------------------------------------------------------------------------+
|i25 : E^8                                                                    |
|                                                                             |
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |  1     |        |        |        |        |        |        |       |
|o25 = |ZZ      |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, 0}  |{1, 0}  |{2, 0}  |{3, 0}  |{4, 0}  |{5, 0}  |{6, 0}  |{7, 0} |
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -1} |{1, -1} |{2, -1} |{3, -1} |{4, -1} |{5, -1} |{6, -1} |{7, -1}|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -2} |{1, -2} |{2, -2} |{3, -2} |{4, -2} |{5, -2} |{6, -2} |{7, -2}|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -3} |{1, -3} |{2, -3} |{3, -3} |{4, -3} |{5, -3} |{6, -3} |{7, -3}|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -4} |{1, -4} |{2, -4} |{3, -4} |{4, -4} |{5, -4} |{6, -4} |{7, -4}|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -5} |{1, -5} |{2, -5} |{3, -5} |{4, -5} |{5, -5} |{6, -5} |{7, -5}|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |        |        |        |        |        |        |        |  1    |
|      |0       |0       |0       |0       |0       |0       |0       |ZZ     |
|      |        |        |        |        |        |        |        |       |
|      |{0, -6} |{1, -6} |{2, -6} |{3, -6} |{4, -6} |{5, -6} |{6, -6} |{7, -6}|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -7} |{1, -7} |{2, -7} |{3, -7} |{4, -7} |{5, -7} |{6, -7} |{7, -7}|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -8} |{1, -8} |{2, -8} |{3, -8} |{4, -8} |{5, -8} |{6, -8} |{7, -8}|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -9} |{1, -9} |{2, -9} |{3, -9} |{4, -9} |{5, -9} |{6, -9} |{7, -9}|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -10}|{1, -10}|{2, -10}|{3, -10}|{4, -10}|{5, -10}|{6, -10}|{7, -10|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -11}|{1, -11}|{2, -11}|{3, -11}|{4, -11}|{5, -11}|{6, -11}|{7, -11|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -12}|{1, -12}|{2, -12}|{3, -12}|{4, -12}|{5, -12}|{6, -12}|{7, -12|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |        |        |        |        |        |        |        |       |
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -13}|{1, -13}|{2, -13}|{3, -13}|{4, -13}|{5, -13}|{6, -13}|{7, -13|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -14}|{1, -14}|{2, -14}|{3, -14}|{4, -14}|{5, -14}|{6, -14}|{7, -14|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |        |        |        |        |        |        |        |       |
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -15}|{1, -15}|{2, -15}|{3, -15}|{4, -15}|{5, -15}|{6, -15}|{7, -15|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|                                                                             |
|o25 : SpectralSequencePage                                                   |
|-----------------------------------------------------------------------------|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |        |        |         |         |         |         |         |       |
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
| |{8, 0}  |{9, 0}  |{10, 0}  |{11, 0}  |{12, 0}  |{13, 0}  |{14, 0}  |{15, 0}|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
| |{8, -1} |{9, -1} |{10, -1} |{11, -1} |{12, -1} |{13, -1} |{14, -1} |{15, -1|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
| |{8, -2} |{9, -2} |{10, -2} |{11, -2} |{12, -2} |{13, -2} |{14, -2} |{15, -2|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
| |{8, -3} |{9, -3} |{10, -3} |{11, -3} |{12, -3} |{13, -3} |{14, -3} |{15, -3|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
| |{8, -4} |{9, -4} |{10, -4} |{11, -4} |{12, -4} |{13, -4} |{14, -4} |{15, -4|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
| |{8, -5} |{9, -5} |{10, -5} |{11, -5} |{12, -5} |{13, -5} |{14, -5} |{15, -5|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |        |        |         |         |         |         |         |       |
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
| |{8, -6} |{9, -6} |{10, -6} |{11, -6} |{12, -6} |{13, -6} |{14, -6} |{15, -6|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
| |{8, -7} |{9, -7} |{10, -7} |{11, -7} |{12, -7} |{13, -7} |{14, -7} |{15, -7|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
| |{8, -8} |{9, -8} |{10, -8} |{11, -8} |{12, -8} |{13, -8} |{14, -8} |{15, -8|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
| |{8, -9} |{9, -9} |{10, -9} |{11, -9} |{12, -9} |{13, -9} |{14, -9} |{15, -9|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
|}|{8, -10}|{9, -10}|{10, -10}|{11, -10}|{12, -10}|{13, -10}|{14, -10}|{15, -1|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
|}|{8, -11}|{9, -11}|{10, -11}|{11, -11}|{12, -11}|{13, -11}|{14, -11}|{15, -1|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
|}|{8, -12}|{9, -12}|{10, -12}|{11, -12}|{12, -12}|{13, -12}|{14, -12}|{15, -1|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |        |        |         |         |         |         |         |  1    |
| |0       |0       |0        |0        |0        |0        |0        |ZZ     |
| |        |        |         |         |         |         |         |       |
|}|{8, -13}|{9, -13}|{10, -13}|{11, -13}|{12, -13}|{13, -13}|{14, -13}|{15, -1|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
|}|{8, -14}|{9, -14}|{10, -14}|{11, -14}|{12, -14}|{13, -14}|{14, -14}|{15, -1|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |        |        |         |         |         |         |         |       |
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
|}|{8, -15}|{9, -15}|{10, -15}|{11, -15}|{12, -15}|{13, -15}|{14, -15}|{15, -1|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
|-----------------------------------------------------------------------------|
|--+---------+---------+                                                      |
|  |         |         |                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|  |{16, 0}  |{17, 0}  |                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|} |{16, -1} |{17, -1} |                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|} |{16, -2} |{17, -2} |                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|} |{16, -3} |{17, -3} |                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|} |{16, -4} |{17, -4} |                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|} |{16, -5} |{17, -5} |                                                      |
|--+---------+---------+                                                      |
|  |         |         |                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|} |{16, -6} |{17, -6} |                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|} |{16, -7} |{17, -7} |                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|} |{16, -8} |{17, -8} |                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|} |{16, -9} |{17, -9} |                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|0}|{16, -10}|{17, -10}|                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|1}|{16, -11}|{17, -11}|                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|2}|{16, -12}|{17, -12}|                                                      |
|--+---------+---------+                                                      |
|  |         |         |                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|3}|{16, -13}|{17, -13}|                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|4}|{16, -14}|{17, -14}|                                                      |
|--+---------+---------+                                                      |
|  |         |  1      |                                                      |
|  |0        |ZZ       |                                                      |
|  |         |         |                                                      |
|5}|{16, -15}|{17, -15}|                                                      |
|--+---------+---------+                                                      |
+-----------------------------------------------------------------------------+
|i26 : E^8 .dd                                                                |
|                                                                             |
|o26 = {3, -4} : 0 <----- 0 : {11, -11}                                       |
|                     0                                                       |
|                                                                             |
|      {3, -3} : 0 <----- 0 : {11, -10}                                       |
|                     0                                                       |
|                                                                             |
|      {3, -2} : 0 <----- 0 : {11, -9}                                        |
|                     0                                                       |
|                                                                             |
|      {2, -4} : 0 <----- 0 : {10, -11}                                       |
|                     0                                                       |
|                                                                             |
|      {2, -3} : 0 <----- 0 : {10, -10}                                       |
|                     0                                                       |
|                                                                             |
|      {2, -2} : 0 <----- 0 : {10, -9}                                        |
|                     0                                                       |
|                                                                             |
|      {2, -1} : 0 <----- 0 : {10, -8}                                        |
|                     0                                                       |
|                                                                             |
|      {1, -3} : 0 <----- 0 : {9, -10}                                        |
|                     0                                                       |
|                                                                             |
|      {1, -2} : 0 <----- 0 : {9, -9}                                         |
|                     0                                                       |
|                                                                             |
|      {1, -1} : 0 <----- 0 : {9, -8}                                         |
|                     0                                                       |
|                                                                             |
|      {1, 0} : 0 <----- 0 : {9, -7}                                          |
|                    0                                                        |
|                                                                             |
|      {0, -2} : 0 <----- 0 : {8, -9}                                         |
|                     0                                                       |
|                                                                             |
|      {0, -1} : 0 <----- 0 : {8, -8}                                         |
|                     0                                                       |
|                                                                             |
|                 1                                                           |
|      {0, 0} : ZZ  <----- 0 : {8, -7}                                        |
|                      0                                                      |
|                                                                             |
|      {0, 1} : 0 <----- 0 : {8, -6}                                          |
|                    0                                                        |
|                                                                             |
|      {-1, -1} : 0 <----- 0 : {7, -8}                                        |
|                      0                                                      |
|                                                                             |
|      {-1, 0} : 0 <----- 0 : {7, -7}                                         |
|                     0                                                       |
|                                                                             |
|                           1                                                 |
|      {-1, 1} : 0 <----- ZZ  : {7, -6}                                       |
|                     0                                                       |
|                                                                             |
|      {-1, 2} : 0 <----- 0 : {7, -5}                                         |
|                     0                                                       |
|                                                                             |
|      {-2, 0} : 0 <----- 0 : {6, -7}                                         |
|                     0                                                       |
|                                                                             |
|      {-2, 1} : 0 <----- 0 : {6, -6}                                         |
|                     0                                                       |
|                                                                             |
|      {-2, 2} : 0 <----- 0 : {6, -5}                                         |
|                     0                                                       |
|                                                                             |
|      {-2, 3} : 0 <----- 0 : {6, -4}                                         |
|                     0                                                       |
|                                                                             |
|      {-3, 1} : 0 <----- 0 : {5, -6}                                         |
|                     0                                                       |
|                                                                             |
|      {-3, 2} : 0 <----- 0 : {5, -5}                                         |
|                     0                                                       |
|                                                                             |
|      {-3, 3} : 0 <----- 0 : {5, -4}                                         |
|                     0                                                       |
|                                                                             |
|      {-3, 4} : 0 <----- 0 : {5, -3}                                         |
|                     0                                                       |
|                                                                             |
|      {-4, 2} : 0 <----- 0 : {4, -5}                                         |
|                     0                                                       |
|                                                                             |
|      {-4, 3} : 0 <----- 0 : {4, -4}                                         |
|                     0                                                       |
|                                                                             |
|      {-4, 4} : 0 <----- 0 : {4, -3}                                         |
|                     0                                                       |
|                                                                             |
|      {-4, 5} : 0 <----- 0 : {4, -2}                                         |
|                     0                                                       |
|                                                                             |
|      {-5, 3} : 0 <----- 0 : {3, -4}                                         |
|                     0                                                       |
|                                                                             |
|      {-5, 4} : 0 <----- 0 : {3, -3}                                         |
|                     0                                                       |
|                                                                             |
|      {-5, 5} : 0 <----- 0 : {3, -2}                                         |
|                     0                                                       |
|                                                                             |
|      {-5, 6} : 0 <----- 0 : {3, -1}                                         |
|                     0                                                       |
|                                                                             |
|      {-6, 4} : 0 <----- 0 : {2, -3}                                         |
|                     0                                                       |
|                                                                             |
|      {-6, 5} : 0 <----- 0 : {2, -2}                                         |
|                     0                                                       |
|                                                                             |
|      {-6, 6} : 0 <----- 0 : {2, -1}                                         |
|                     0                                                       |
|                                                                             |
|      {-6, 7} : 0 <----- 0 : {2, 0}                                          |
|                     0                                                       |
|                                                                             |
|      {9, -11} : 0 <----- 0 : {17, -18}                                      |
|                      0                                                      |
|                                                                             |
|      {-7, 5} : 0 <----- 0 : {1, -2}                                         |
|                     0                                                       |
|                                                                             |
|      {9, -10} : 0 <----- 0 : {17, -17}                                      |
|                      0                                                      |
|                                                                             |
|      {-7, 6} : 0 <----- 0 : {1, -1}                                         |
|                     0                                                       |
|                                                                             |
|      {9, -9} : 0 <----- 0 : {17, -16}                                       |
|                     0                                                       |
|                                                                             |
|      {-7, 7} : 0 <----- 0 : {1, 0}                                          |
|                     0                                                       |
|                                                                             |
|                           1                                                 |
|      {9, -8} : 0 <----- ZZ  : {17, -15}                                     |
|                     0                                                       |
|                                                                             |
|      {-7, 8} : 0 <----- 0 : {1, 1}                                          |
|                     0                                                       |
|                                                                             |
|      {8, -10} : 0 <----- 0 : {16, -17}                                      |
|                      0                                                      |
|                                                                             |
|      {-8, 6} : 0 <----- 0 : {0, -1}                                         |
|                     0                                                       |
|                                                                             |
|      {8, -9} : 0 <----- 0 : {16, -16}                                       |
|                     0                                                       |
|                                                                             |
|                           1                                                 |
|      {-8, 7} : 0 <----- ZZ  : {0, 0}                                        |
|                     0                                                       |
|                                                                             |
|      {8, -8} : 0 <----- 0 : {16, -15}                                       |
|                     0                                                       |
|                                                                             |
|      {-8, 8} : 0 <----- 0 : {0, 1}                                          |
|                     0                                                       |
|                                                                             |
|      {8, -7} : 0 <----- 0 : {16, -14}                                       |
|                     0                                                       |
|                                                                             |
|      {-8, 9} : 0 <----- 0 : {0, 2}                                          |
|                     0                                                       |
|                                                                             |
|      {7, -9} : 0 <----- 0 : {15, -16}                                       |
|                     0                                                       |
|                                                                             |
|      {-9, 7} : 0 <----- 0 : {-1, 0}                                         |
|                     0                                                       |
|                                                                             |
|      {7, -8} : 0 <----- 0 : {15, -15}                                       |
|                     0                                                       |
|                                                                             |
|      {-9, 8} : 0 <----- 0 : {-1, 1}                                         |
|                     0                                                       |
|                                                                             |
|      {7, -7} : 0 <----- 0 : {15, -14}                                       |
|                     0                                                       |
|                                                                             |
|      {-9, 9} : 0 <----- 0 : {-1, 2}                                         |
|                     0                                                       |
|                                                                             |
|                  1               1                                          |
|      {7, -6} : ZZ  <---------- ZZ  : {15, -13}                              |
|                       | -1 |                                                |
|                                                                             |
|      {-9, 10} : 0 <----- 0 : {-1, 3}                                        |
|                      0                                                      |
|                                                                             |
|      {6, -8} : 0 <----- 0 : {14, -15}                                       |
|                     0                                                       |
|                                                                             |
|      {6, -7} : 0 <----- 0 : {14, -14}                                       |
|                     0                                                       |
|                                                                             |
|      {6, -6} : 0 <----- 0 : {14, -13}                                       |
|                     0                                                       |
|                                                                             |
|      {6, -5} : 0 <----- 0 : {14, -12}                                       |
|                     0                                                       |
|                                                                             |
|      {5, -7} : 0 <----- 0 : {13, -14}                                       |
|                     0                                                       |
|                                                                             |
|      {5, -6} : 0 <----- 0 : {13, -13}                                       |
|                     0                                                       |
|                                                                             |
|      {5, -5} : 0 <----- 0 : {13, -12}                                       |
|                     0                                                       |
|                                                                             |
|      {5, -4} : 0 <----- 0 : {13, -11}                                       |
|                     0                                                       |
|                                                                             |
|      {4, -6} : 0 <----- 0 : {12, -13}                                       |
|                     0                                                       |
|                                                                             |
|      {4, -5} : 0 <----- 0 : {12, -12}                                       |
|                     0                                                       |
|                                                                             |
|      {4, -4} : 0 <----- 0 : {12, -11}                                       |
|                     0                                                       |
|                                                                             |
|      {4, -3} : 0 <----- 0 : {12, -10}                                       |
|                     0                                                       |
|                                                                             |
|      {3, -5} : 0 <----- 0 : {11, -12}                                       |
|                     0                                                       |
|                                                                             |
|o26 : SpectralSequencePageMap                                                |
+-----------------------------------------------------------------------------+
|i27 : E^9                                                                    |
|                                                                             |
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |  1     |        |        |        |        |        |        |       |
|o27 = |ZZ      |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, 0}  |{1, 0}  |{2, 0}  |{3, 0}  |{4, 0}  |{5, 0}  |{6, 0}  |{7, 0} |
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -1} |{1, -1} |{2, -1} |{3, -1} |{4, -1} |{5, -1} |{6, -1} |{7, -1}|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -2} |{1, -2} |{2, -2} |{3, -2} |{4, -2} |{5, -2} |{6, -2} |{7, -2}|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -3} |{1, -3} |{2, -3} |{3, -3} |{4, -3} |{5, -3} |{6, -3} |{7, -3}|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -4} |{1, -4} |{2, -4} |{3, -4} |{4, -4} |{5, -4} |{6, -4} |{7, -4}|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -5} |{1, -5} |{2, -5} |{3, -5} |{4, -5} |{5, -5} |{6, -5} |{7, -5}|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -6} |{1, -6} |{2, -6} |{3, -6} |{4, -6} |{5, -6} |{6, -6} |{7, -6}|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -7} |{1, -7} |{2, -7} |{3, -7} |{4, -7} |{5, -7} |{6, -7} |{7, -7}|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -8} |{1, -8} |{2, -8} |{3, -8} |{4, -8} |{5, -8} |{6, -8} |{7, -8}|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -9} |{1, -9} |{2, -9} |{3, -9} |{4, -9} |{5, -9} |{6, -9} |{7, -9}|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -10}|{1, -10}|{2, -10}|{3, -10}|{4, -10}|{5, -10}|{6, -10}|{7, -10|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -11}|{1, -11}|{2, -11}|{3, -11}|{4, -11}|{5, -11}|{6, -11}|{7, -11|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -12}|{1, -12}|{2, -12}|{3, -12}|{4, -12}|{5, -12}|{6, -12}|{7, -12|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -13}|{1, -13}|{2, -13}|{3, -13}|{4, -13}|{5, -13}|{6, -13}|{7, -13|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -14}|{1, -14}|{2, -14}|{3, -14}|{4, -14}|{5, -14}|{6, -14}|{7, -14|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |        |        |        |        |        |        |        |       |
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -15}|{1, -15}|{2, -15}|{3, -15}|{4, -15}|{5, -15}|{6, -15}|{7, -15|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|                                                                             |
|o27 : SpectralSequencePage                                                   |
|-----------------------------------------------------------------------------|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |        |        |         |         |         |         |         |       |
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
| |{8, 0}  |{9, 0}  |{10, 0}  |{11, 0}  |{12, 0}  |{13, 0}  |{14, 0}  |{15, 0}|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
| |{8, -1} |{9, -1} |{10, -1} |{11, -1} |{12, -1} |{13, -1} |{14, -1} |{15, -1|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
| |{8, -2} |{9, -2} |{10, -2} |{11, -2} |{12, -2} |{13, -2} |{14, -2} |{15, -2|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
| |{8, -3} |{9, -3} |{10, -3} |{11, -3} |{12, -3} |{13, -3} |{14, -3} |{15, -3|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
| |{8, -4} |{9, -4} |{10, -4} |{11, -4} |{12, -4} |{13, -4} |{14, -4} |{15, -4|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
| |{8, -5} |{9, -5} |{10, -5} |{11, -5} |{12, -5} |{13, -5} |{14, -5} |{15, -5|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
| |{8, -6} |{9, -6} |{10, -6} |{11, -6} |{12, -6} |{13, -6} |{14, -6} |{15, -6|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
| |{8, -7} |{9, -7} |{10, -7} |{11, -7} |{12, -7} |{13, -7} |{14, -7} |{15, -7|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
| |{8, -8} |{9, -8} |{10, -8} |{11, -8} |{12, -8} |{13, -8} |{14, -8} |{15, -8|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
| |{8, -9} |{9, -9} |{10, -9} |{11, -9} |{12, -9} |{13, -9} |{14, -9} |{15, -9|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
|}|{8, -10}|{9, -10}|{10, -10}|{11, -10}|{12, -10}|{13, -10}|{14, -10}|{15, -1|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
|}|{8, -11}|{9, -11}|{10, -11}|{11, -11}|{12, -11}|{13, -11}|{14, -11}|{15, -1|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
|}|{8, -12}|{9, -12}|{10, -12}|{11, -12}|{12, -12}|{13, -12}|{14, -12}|{15, -1|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
|}|{8, -13}|{9, -13}|{10, -13}|{11, -13}|{12, -13}|{13, -13}|{14, -13}|{15, -1|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
|}|{8, -14}|{9, -14}|{10, -14}|{11, -14}|{12, -14}|{13, -14}|{14, -14}|{15, -1|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |        |        |         |         |         |         |         |       |
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
|}|{8, -15}|{9, -15}|{10, -15}|{11, -15}|{12, -15}|{13, -15}|{14, -15}|{15, -1|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
|-----------------------------------------------------------------------------|
|--+---------+---------+                                                      |
|  |         |         |                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|  |{16, 0}  |{17, 0}  |                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|} |{16, -1} |{17, -1} |                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|} |{16, -2} |{17, -2} |                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|} |{16, -3} |{17, -3} |                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|} |{16, -4} |{17, -4} |                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|} |{16, -5} |{17, -5} |                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|} |{16, -6} |{17, -6} |                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|} |{16, -7} |{17, -7} |                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|} |{16, -8} |{17, -8} |                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|} |{16, -9} |{17, -9} |                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|0}|{16, -10}|{17, -10}|                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|1}|{16, -11}|{17, -11}|                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|2}|{16, -12}|{17, -12}|                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|3}|{16, -13}|{17, -13}|                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|4}|{16, -14}|{17, -14}|                                                      |
|--+---------+---------+                                                      |
|  |         |  1      |                                                      |
|  |0        |ZZ       |                                                      |
|  |         |         |                                                      |
|5}|{16, -15}|{17, -15}|                                                      |
|--+---------+---------+                                                      |
+-----------------------------------------------------------------------------+
|i28 : E^9 .dd                                                                |
|                                                                             |
|o28 = {2, -3} : 0 <----- 0 : {11, -11}                                       |
|                     0                                                       |
|                                                                             |
|      {2, -2} : 0 <----- 0 : {11, -10}                                       |
|                     0                                                       |
|                                                                             |
|      {2, -1} : 0 <----- 0 : {11, -9}                                        |
|                     0                                                       |
|                                                                             |
|      {1, -3} : 0 <----- 0 : {10, -11}                                       |
|                     0                                                       |
|                                                                             |
|      {1, -2} : 0 <----- 0 : {10, -10}                                       |
|                     0                                                       |
|                                                                             |
|      {1, -1} : 0 <----- 0 : {10, -9}                                        |
|                     0                                                       |
|                                                                             |
|      {1, 0} : 0 <----- 0 : {10, -8}                                         |
|                    0                                                        |
|                                                                             |
|      {0, -2} : 0 <----- 0 : {9, -10}                                        |
|                     0                                                       |
|                                                                             |
|      {0, -1} : 0 <----- 0 : {9, -9}                                         |
|                     0                                                       |
|                                                                             |
|                 1                                                           |
|      {0, 0} : ZZ  <----- 0 : {9, -8}                                        |
|                      0                                                      |
|                                                                             |
|      {0, 1} : 0 <----- 0 : {9, -7}                                          |
|                    0                                                        |
|                                                                             |
|      {-1, -1} : 0 <----- 0 : {8, -9}                                        |
|                      0                                                      |
|                                                                             |
|      {-1, 0} : 0 <----- 0 : {8, -8}                                         |
|                     0                                                       |
|                                                                             |
|      {-1, 1} : 0 <----- 0 : {8, -7}                                         |
|                     0                                                       |
|                                                                             |
|      {-1, 2} : 0 <----- 0 : {8, -6}                                         |
|                     0                                                       |
|                                                                             |
|      {-2, 0} : 0 <----- 0 : {7, -8}                                         |
|                     0                                                       |
|                                                                             |
|      {-2, 1} : 0 <----- 0 : {7, -7}                                         |
|                     0                                                       |
|                                                                             |
|      {-2, 2} : 0 <----- 0 : {7, -6}                                         |
|                     0                                                       |
|                                                                             |
|      {-2, 3} : 0 <----- 0 : {7, -5}                                         |
|                     0                                                       |
|                                                                             |
|      {-3, 1} : 0 <----- 0 : {6, -7}                                         |
|                     0                                                       |
|                                                                             |
|      {-3, 2} : 0 <----- 0 : {6, -6}                                         |
|                     0                                                       |
|                                                                             |
|      {-3, 3} : 0 <----- 0 : {6, -5}                                         |
|                     0                                                       |
|                                                                             |
|      {-3, 4} : 0 <----- 0 : {6, -4}                                         |
|                     0                                                       |
|                                                                             |
|      {-4, 2} : 0 <----- 0 : {5, -6}                                         |
|                     0                                                       |
|                                                                             |
|      {-4, 3} : 0 <----- 0 : {5, -5}                                         |
|                     0                                                       |
|                                                                             |
|      {-4, 4} : 0 <----- 0 : {5, -4}                                         |
|                     0                                                       |
|                                                                             |
|      {-4, 5} : 0 <----- 0 : {5, -3}                                         |
|                     0                                                       |
|                                                                             |
|      {-5, 3} : 0 <----- 0 : {4, -5}                                         |
|                     0                                                       |
|                                                                             |
|      {-5, 4} : 0 <----- 0 : {4, -4}                                         |
|                     0                                                       |
|                                                                             |
|      {-5, 5} : 0 <----- 0 : {4, -3}                                         |
|                     0                                                       |
|                                                                             |
|      {-5, 6} : 0 <----- 0 : {4, -2}                                         |
|                     0                                                       |
|                                                                             |
|      {-6, 4} : 0 <----- 0 : {3, -4}                                         |
|                     0                                                       |
|                                                                             |
|      {-6, 5} : 0 <----- 0 : {3, -3}                                         |
|                     0                                                       |
|                                                                             |
|      {-6, 6} : 0 <----- 0 : {3, -2}                                         |
|                     0                                                       |
|                                                                             |
|      {-6, 7} : 0 <----- 0 : {3, -1}                                         |
|                     0                                                       |
|                                                                             |
|      {-7, 5} : 0 <----- 0 : {2, -3}                                         |
|                     0                                                       |
|                                                                             |
|      {-7, 6} : 0 <----- 0 : {2, -2}                                         |
|                     0                                                       |
|                                                                             |
|      {-7, 7} : 0 <----- 0 : {2, -1}                                         |
|                     0                                                       |
|                                                                             |
|      {-7, 8} : 0 <----- 0 : {2, 0}                                          |
|                     0                                                       |
|                                                                             |
|      {8, -10} : 0 <----- 0 : {17, -18}                                      |
|                      0                                                      |
|                                                                             |
|      {-8, 6} : 0 <----- 0 : {1, -2}                                         |
|                     0                                                       |
|                                                                             |
|      {8, -9} : 0 <----- 0 : {17, -17}                                       |
|                     0                                                       |
|                                                                             |
|      {-8, 7} : 0 <----- 0 : {1, -1}                                         |
|                     0                                                       |
|                                                                             |
|      {8, -8} : 0 <----- 0 : {17, -16}                                       |
|                     0                                                       |
|                                                                             |
|      {-8, 8} : 0 <----- 0 : {1, 0}                                          |
|                     0                                                       |
|                                                                             |
|                           1                                                 |
|      {8, -7} : 0 <----- ZZ  : {17, -15}                                     |
|                     0                                                       |
|                                                                             |
|      {-8, 9} : 0 <----- 0 : {1, 1}                                          |
|                     0                                                       |
|                                                                             |
|      {7, -9} : 0 <----- 0 : {16, -17}                                       |
|                     0                                                       |
|                                                                             |
|      {-9, 7} : 0 <----- 0 : {0, -1}                                         |
|                     0                                                       |
|                                                                             |
|      {7, -8} : 0 <----- 0 : {16, -16}                                       |
|                     0                                                       |
|                                                                             |
|                           1                                                 |
|      {-9, 8} : 0 <----- ZZ  : {0, 0}                                        |
|                     0                                                       |
|                                                                             |
|      {7, -7} : 0 <----- 0 : {16, -15}                                       |
|                     0                                                       |
|                                                                             |
|      {-9, 9} : 0 <----- 0 : {0, 1}                                          |
|                     0                                                       |
|                                                                             |
|      {7, -6} : 0 <----- 0 : {16, -14}                                       |
|                     0                                                       |
|                                                                             |
|      {-9, 10} : 0 <----- 0 : {0, 2}                                         |
|                      0                                                      |
|                                                                             |
|      {6, -8} : 0 <----- 0 : {15, -16}                                       |
|                     0                                                       |
|                                                                             |
|      {-10, 8} : 0 <----- 0 : {-1, 0}                                        |
|                      0                                                      |
|                                                                             |
|      {6, -7} : 0 <----- 0 : {15, -15}                                       |
|                     0                                                       |
|                                                                             |
|      {-10, 9} : 0 <----- 0 : {-1, 1}                                        |
|                      0                                                      |
|                                                                             |
|      {6, -6} : 0 <----- 0 : {15, -14}                                       |
|                     0                                                       |
|                                                                             |
|      {-10, 10} : 0 <----- 0 : {-1, 2}                                       |
|                       0                                                     |
|                                                                             |
|      {6, -5} : 0 <----- 0 : {15, -13}                                       |
|                     0                                                       |
|                                                                             |
|      {-10, 11} : 0 <----- 0 : {-1, 3}                                       |
|                       0                                                     |
|                                                                             |
|      {5, -7} : 0 <----- 0 : {14, -15}                                       |
|                     0                                                       |
|                                                                             |
|      {5, -6} : 0 <----- 0 : {14, -14}                                       |
|                     0                                                       |
|                                                                             |
|      {5, -5} : 0 <----- 0 : {14, -13}                                       |
|                     0                                                       |
|                                                                             |
|      {5, -4} : 0 <----- 0 : {14, -12}                                       |
|                     0                                                       |
|                                                                             |
|      {4, -6} : 0 <----- 0 : {13, -14}                                       |
|                     0                                                       |
|                                                                             |
|      {4, -5} : 0 <----- 0 : {13, -13}                                       |
|                     0                                                       |
|                                                                             |
|      {4, -4} : 0 <----- 0 : {13, -12}                                       |
|                     0                                                       |
|                                                                             |
|      {4, -3} : 0 <----- 0 : {13, -11}                                       |
|                     0                                                       |
|                                                                             |
|      {3, -5} : 0 <----- 0 : {12, -13}                                       |
|                     0                                                       |
|                                                                             |
|      {3, -4} : 0 <----- 0 : {12, -12}                                       |
|                     0                                                       |
|                                                                             |
|      {3, -3} : 0 <----- 0 : {12, -11}                                       |
|                     0                                                       |
|                                                                             |
|      {3, -2} : 0 <----- 0 : {12, -10}                                       |
|                     0                                                       |
|                                                                             |
|      {2, -4} : 0 <----- 0 : {11, -12}                                       |
|                     0                                                       |
|                                                                             |
|o28 : SpectralSequencePageMap                                                |
+-----------------------------------------------------------------------------+
|i29 : E^infinity                                                             |
|                                                                             |
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |  1     |        |        |        |        |        |        |       |
|o29 = |ZZ      |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, 0}  |{1, 0}  |{2, 0}  |{3, 0}  |{4, 0}  |{5, 0}  |{6, 0}  |{7, 0} |
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -1} |{1, -1} |{2, -1} |{3, -1} |{4, -1} |{5, -1} |{6, -1} |{7, -1}|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -2} |{1, -2} |{2, -2} |{3, -2} |{4, -2} |{5, -2} |{6, -2} |{7, -2}|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -3} |{1, -3} |{2, -3} |{3, -3} |{4, -3} |{5, -3} |{6, -3} |{7, -3}|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -4} |{1, -4} |{2, -4} |{3, -4} |{4, -4} |{5, -4} |{6, -4} |{7, -4}|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -5} |{1, -5} |{2, -5} |{3, -5} |{4, -5} |{5, -5} |{6, -5} |{7, -5}|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -6} |{1, -6} |{2, -6} |{3, -6} |{4, -6} |{5, -6} |{6, -6} |{7, -6}|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -7} |{1, -7} |{2, -7} |{3, -7} |{4, -7} |{5, -7} |{6, -7} |{7, -7}|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -8} |{1, -8} |{2, -8} |{3, -8} |{4, -8} |{5, -8} |{6, -8} |{7, -8}|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -9} |{1, -9} |{2, -9} |{3, -9} |{4, -9} |{5, -9} |{6, -9} |{7, -9}|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -10}|{1, -10}|{2, -10}|{3, -10}|{4, -10}|{5, -10}|{6, -10}|{7, -10|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -11}|{1, -11}|{2, -11}|{3, -11}|{4, -11}|{5, -11}|{6, -11}|{7, -11|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -12}|{1, -12}|{2, -12}|{3, -12}|{4, -12}|{5, -12}|{6, -12}|{7, -12|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -13}|{1, -13}|{2, -13}|{3, -13}|{4, -13}|{5, -13}|{6, -13}|{7, -13|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -14}|{1, -14}|{2, -14}|{3, -14}|{4, -14}|{5, -14}|{6, -14}|{7, -14|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|      |        |        |        |        |        |        |        |       |
|      |0       |0       |0       |0       |0       |0       |0       |0      |
|      |        |        |        |        |        |        |        |       |
|      |{0, -15}|{1, -15}|{2, -15}|{3, -15}|{4, -15}|{5, -15}|{6, -15}|{7, -15|
|      +--------+--------+--------+--------+--------+--------+--------+-------|
|                                                                             |
|o29 : Page                                                                   |
|-----------------------------------------------------------------------------|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |        |        |         |         |         |         |         |       |
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
| |{8, 0}  |{9, 0}  |{10, 0}  |{11, 0}  |{12, 0}  |{13, 0}  |{14, 0}  |{15, 0}|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
| |{8, -1} |{9, -1} |{10, -1} |{11, -1} |{12, -1} |{13, -1} |{14, -1} |{15, -1|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
| |{8, -2} |{9, -2} |{10, -2} |{11, -2} |{12, -2} |{13, -2} |{14, -2} |{15, -2|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
| |{8, -3} |{9, -3} |{10, -3} |{11, -3} |{12, -3} |{13, -3} |{14, -3} |{15, -3|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
| |{8, -4} |{9, -4} |{10, -4} |{11, -4} |{12, -4} |{13, -4} |{14, -4} |{15, -4|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
| |{8, -5} |{9, -5} |{10, -5} |{11, -5} |{12, -5} |{13, -5} |{14, -5} |{15, -5|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
| |{8, -6} |{9, -6} |{10, -6} |{11, -6} |{12, -6} |{13, -6} |{14, -6} |{15, -6|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
| |{8, -7} |{9, -7} |{10, -7} |{11, -7} |{12, -7} |{13, -7} |{14, -7} |{15, -7|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
| |{8, -8} |{9, -8} |{10, -8} |{11, -8} |{12, -8} |{13, -8} |{14, -8} |{15, -8|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
| |{8, -9} |{9, -9} |{10, -9} |{11, -9} |{12, -9} |{13, -9} |{14, -9} |{15, -9|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
|}|{8, -10}|{9, -10}|{10, -10}|{11, -10}|{12, -10}|{13, -10}|{14, -10}|{15, -1|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
|}|{8, -11}|{9, -11}|{10, -11}|{11, -11}|{12, -11}|{13, -11}|{14, -11}|{15, -1|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
|}|{8, -12}|{9, -12}|{10, -12}|{11, -12}|{12, -12}|{13, -12}|{14, -12}|{15, -1|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
|}|{8, -13}|{9, -13}|{10, -13}|{11, -13}|{12, -13}|{13, -13}|{14, -13}|{15, -1|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
|}|{8, -14}|{9, -14}|{10, -14}|{11, -14}|{12, -14}|{13, -14}|{14, -14}|{15, -1|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
| |        |        |         |         |         |         |         |       |
| |0       |0       |0        |0        |0        |0        |0        |0      |
| |        |        |         |         |         |         |         |       |
|}|{8, -15}|{9, -15}|{10, -15}|{11, -15}|{12, -15}|{13, -15}|{14, -15}|{15, -1|
|-+--------+--------+---------+---------+---------+---------+---------+-------|
|-----------------------------------------------------------------------------|
|--+---------+---------+                                                      |
|  |         |         |                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|  |{16, 0}  |{17, 0}  |                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|} |{16, -1} |{17, -1} |                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|} |{16, -2} |{17, -2} |                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|} |{16, -3} |{17, -3} |                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|} |{16, -4} |{17, -4} |                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|} |{16, -5} |{17, -5} |                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|} |{16, -6} |{17, -6} |                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|} |{16, -7} |{17, -7} |                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|} |{16, -8} |{17, -8} |                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|} |{16, -9} |{17, -9} |                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|0}|{16, -10}|{17, -10}|                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|1}|{16, -11}|{17, -11}|                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|2}|{16, -12}|{17, -12}|                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|3}|{16, -13}|{17, -13}|                                                      |
|--+---------+---------+                                                      |
|  |0        |0        |                                                      |
|  |         |         |                                                      |
|4}|{16, -14}|{17, -14}|                                                      |
|--+---------+---------+                                                      |
|  |         |  1      |                                                      |
|  |0        |ZZ       |                                                      |
|  |         |         |                                                      |
|5}|{16, -15}|{17, -15}|                                                      |
|--+---------+---------+                                                      |
+-----------------------------------------------------------------------------+
|i30 : prune HH K_infinity                                                    |
|                                                                             |
|o30 = -1 : 0                                                                 |
|                                                                             |
|             1                                                               |
|       0 : ZZ                                                                |
|                                                                             |
|       1 : 0                                                                 |
|                                                                             |
|             1                                                               |
|       2 : ZZ                                                                |
|                                                                             |
|o30 : GradedModule                                                           |
+-----------------------------------------------------------------------------+
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:1496:0.

associatedGradedHomologyObject -- compute the associated graded homology object
*******************************************************************************

  * Usage:
        M = associatedGradedHomologyObject(ZZ, ZZ, FilteredComplex)
  * Inputs:
      * p, an integer (Macaulay2Doc),
      * n, an integer (Macaulay2Doc),
      * K, a filtered chain complex,
  * Outputs:
      * M, a module (Macaulay2Doc),

Description
===========

Computes the associated graded homology object determined by the filtered chain
complex

Ways to use associatedGradedHomologyObject:
===========================================

  * "associatedGradedHomologyObject(ZZ,ZZ,FilteredComplex)"

For the programmer
==================

The object associatedGradedHomologyObject,
is a method function (Macaulay2Doc).

-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:3906:0.

Balancing Tor
*************

To balance Tor we first need to make some modules over a ring.

+---------------------------------------+
|i1 : A = QQ[x,y,z,w];                  |
+---------------------------------------+
|i2 : M = monomialCurveIdeal(A,{1,2,3});|
|                                       |
|o2 : Ideal of A                        |
+---------------------------------------+
|i3 : N = monomialCurveIdeal(A,{1,3,4});|
|                                       |
|o3 : Ideal of A                        |
+---------------------------------------+

To compute $Tor^A_i(M,N)$ we resolve the modules, tensor appropriately, and
then take homology.

+----------------------------------+
|i4 : K = res M                    |
|                                  |
|      1      3      2             |
|o4 = A  <-- A  <-- A  <-- 0       |
|                                  |
|     0      1      2      3       |
|                                  |
|o4 : ChainComplex                 |
+----------------------------------+
|i5 : J = res N                    |
|                                  |
|      1      4      4      1      |
|o5 = A  <-- A  <-- A  <-- A  <-- 0|
|                                  |
|     0      1      2      3      4|
|                                  |
|o5 : ChainComplex                 |
+----------------------------------+

The spectral sequence that computes $Tor^A_i(M,N)$ by tensoring $K$ with $N$
and taking homology is given by

+---------------------------------------------------------+
|i6 : E = prune spectralSequence((filteredComplex K) ** J)|
|                                                         |
|o6 = E                                                   |
|                                                         |
|o6 : SpectralSequence                                    |
+---------------------------------------------------------+

The spectral sequence that computes $Tor^A_i(M,N)$ by tensoring $J$ with $M$
and taking homology is given by

+-----------------------------------------------------------+
|i7 : F = prune spectralSequence((K ** (filteredComplex J)))|
|                                                           |
|o7 = F                                                     |
|                                                           |
|o7 : SpectralSequence                                      |
+-----------------------------------------------------------+

Let's compute some pages and maps of these spectral sequences. The zeroth pages
takes the form:

+-----------------------------------------------------------------------------+
|i8 : E^0                                                                     |
|                                                                             |
|     +------+------+------+                                                  |
|     | 1    | 3    | 2    |                                                  |
|o8 = |A     |A     |A     |                                                  |
|     |      |      |      |                                                  |
|     |{0, 3}|{1, 3}|{2, 3}|                                                  |
|     +------+------+------+                                                  |
|     | 4    | 12   | 8    |                                                  |
|     |A     |A     |A     |                                                  |
|     |      |      |      |                                                  |
|     |{0, 2}|{1, 2}|{2, 2}|                                                  |
|     +------+------+------+                                                  |
|     | 4    | 12   | 8    |                                                  |
|     |A     |A     |A     |                                                  |
|     |      |      |      |                                                  |
|     |{0, 1}|{1, 1}|{2, 1}|                                                  |
|     +------+------+------+                                                  |
|     | 1    | 3    | 2    |                                                  |
|     |A     |A     |A     |                                                  |
|     |      |      |      |                                                  |
|     |{0, 0}|{1, 0}|{2, 0}|                                                  |
|     +------+------+------+                                                  |
|                                                                             |
|o8 : SpectralSequencePage                                                    |
+-----------------------------------------------------------------------------+
|i9 : E^0 .dd                                                                 |
|                                                                             |
|o9 = {2, -3} : 0 <----- 0 : {2, -2}                                          |
|                    0                                                        |
|                                                                             |
|     {2, -2} : 0 <----- 0 : {2, -1}                                          |
|                    0                                                        |
|                                                                             |
|                         2                                                   |
|     {2, -1} : 0 <----- A  : {2, 0}                                          |
|                    0                                                        |
|                                                                             |
|               2                                                             |
|     {2, 0} : A  <-----------------------------------------------------------|
|                    {3} | yz-xw y3-x2z xz2-y2w z3-yw2 0     0      0       0 |
|                    {3} | 0     0      0       0      yz-xw y3-x2z xz2-y2w z3|
|                                                                             |
|               8                                               8             |
|     {2, 1} : A  <------------------------------------------- A  : {2, 2}    |
|                    {5} | -y2 -xz -yw -z2 0   0   0   0   |                  |
|                    {6} | z   w   0   0   0   0   0   0   |                  |
|                    {6} | x   y   -z  -w  0   0   0   0   |                  |
|                    {6} | 0   0   x   y   0   0   0   0   |                  |
|                    {5} | 0   0   0   0   -y2 -xz -yw -z2 |                  |
|                    {6} | 0   0   0   0   z   w   0   0   |                  |
|                    {6} | 0   0   0   0   x   y   -z  -w  |                  |
|                    {6} | 0   0   0   0   0   0   x   y   |                  |
|                                                                             |
|               8                     2                                       |
|     {2, 2} : A  <----------------- A  : {2, 3}                              |
|                    {7} | w  0  |                                            |
|                    {7} | -z 0  |                                            |
|                    {7} | -y 0  |                                            |
|                    {7} | x  0  |                                            |
|                    {7} | 0  w  |                                            |
|                    {7} | 0  -z |                                            |
|                    {7} | 0  -y |                                            |
|                    {7} | 0  x  |                                            |
|                                                                             |
|               2                                                             |
|     {2, 3} : A  <----- 0 : {2, 4}                                           |
|                    0                                                        |
|                                                                             |
|     {2, 4} : 0 <----- 0 : {2, 5}                                            |
|                   0                                                         |
|                                                                             |
|     {1, -2} : 0 <----- 0 : {1, -1}                                          |
|                    0                                                        |
|                                                                             |
|                         3                                                   |
|     {1, -1} : 0 <----- A  : {1, 0}                                          |
|                    0                                                        |
|                                                                             |
|               3                                                             |
|     {1, 0} : A  <-----------------------------------------------------------|
|                    {2} | -yz+xw -y3+x2z -xz2+y2w -z3+yw2 0      0       0   |
|                    {2} | 0      0       0        0       -yz+xw -y3+x2z -xz2|
|                    {2} | 0      0       0        0       0      0       0   |
|                                                                             |
|               12                                                   12       |
|     {1, 1} : A   <----------------------------------------------- A   : {1, |
|                     {4} | y2 xz yw z2 0  0  0  0  0  0  0  0  |             |
|                     {5} | -z -w 0  0  0  0  0  0  0  0  0  0  |             |
|                     {5} | -x -y z  w  0  0  0  0  0  0  0  0  |             |
|                     {5} | 0  0  -x -y 0  0  0  0  0  0  0  0  |             |
|                     {4} | 0  0  0  0  y2 xz yw z2 0  0  0  0  |             |
|                     {5} | 0  0  0  0  -z -w 0  0  0  0  0  0  |             |
|                     {5} | 0  0  0  0  -x -y z  w  0  0  0  0  |             |
|                     {5} | 0  0  0  0  0  0  -x -y 0  0  0  0  |             |
|                     {4} | 0  0  0  0  0  0  0  0  y2 xz yw z2 |             |
|                     {5} | 0  0  0  0  0  0  0  0  -z -w 0  0  |             |
|                     {5} | 0  0  0  0  0  0  0  0  -x -y z  w  |             |
|                     {5} | 0  0  0  0  0  0  0  0  0  0  -x -y |             |
|                                                                             |
|               12                        3                                   |
|     {1, 2} : A   <-------------------- A  : {1, 3}                          |
|                     {6} | -w 0  0  |                                        |
|                     {6} | z  0  0  |                                        |
|                     {6} | y  0  0  |                                        |
|                     {6} | -x 0  0  |                                        |
|                     {6} | 0  -w 0  |                                        |
|                     {6} | 0  z  0  |                                        |
|                     {6} | 0  y  0  |                                        |
|                     {6} | 0  -x 0  |                                        |
|                     {6} | 0  0  -w |                                        |
|                     {6} | 0  0  z  |                                        |
|                     {6} | 0  0  y  |                                        |
|                     {6} | 0  0  -x |                                        |
|                                                                             |
|               3                                                             |
|     {1, 3} : A  <----- 0 : {1, 4}                                           |
|                    0                                                        |
|                                                                             |
|     {1, 4} : 0 <----- 0 : {1, 5}                                            |
|                   0                                                         |
|                                                                             |
|     {1, 5} : 0 <----- 0 : {1, 6}                                            |
|                   0                                                         |
|                                                                             |
|                         1                                                   |
|     {0, -1} : 0 <----- A  : {0, 0}                                          |
|                    0                                                        |
|                                                                             |
|               1                                       4                     |
|     {0, 0} : A  <----------------------------------- A  : {0, 1}            |
|                    | yz-xw y3-x2z xz2-y2w z3-yw2 |                          |
|                                                                             |
|               4                               4                             |
|     {0, 1} : A  <--------------------------- A  : {0, 2}                    |
|                    {2} | -y2 -xz -yw -z2 |                                  |
|                    {3} | z   w   0   0   |                                  |
|                    {3} | x   y   -z  -w  |                                  |
|                    {3} | 0   0   x   y   |                                  |
|                                                                             |
|               4                  1                                          |
|     {0, 2} : A  <-------------- A  : {0, 3}                                 |
|                    {4} | w  |                                               |
|                    {4} | -z |                                               |
|                    {4} | -y |                                               |
|                    {4} | x  |                                               |
|                                                                             |
|               1                                                             |
|     {0, 3} : A  <----- 0 : {0, 4}                                           |
|                    0                                                        |
|                                                                             |
|     {0, 4} : 0 <----- 0 : {0, 5}                                            |
|                   0                                                         |
|                                                                             |
|     {0, 5} : 0 <----- 0 : {0, 6}                                            |
|                   0                                                         |
|                                                                             |
|     {0, 6} : 0 <----- 0 : {0, 7}                                            |
|                   0                                                         |
|                                                                             |
|     {-1, 0} : 0 <----- 0 : {-1, 1}                                          |
|                    0                                                        |
|                                                                             |
|     {-1, 1} : 0 <----- 0 : {-1, 2}                                          |
|                    0                                                        |
|                                                                             |
|     {-1, 2} : 0 <----- 0 : {-1, 3}                                          |
|                    0                                                        |
|                                                                             |
|     {-1, 3} : 0 <----- 0 : {-1, 4}                                          |
|                    0                                                        |
|                                                                             |
|     {-1, 4} : 0 <----- 0 : {-1, 5}                                          |
|                    0                                                        |
|                                                                             |
|     {-1, 5} : 0 <----- 0 : {-1, 6}                                          |
|                    0                                                        |
|                                                                             |
|     {-1, 6} : 0 <----- 0 : {-1, 7}                                          |
|                    0                                                        |
|                                                                             |
|     {-1, 7} : 0 <----- 0 : {-1, 8}                                          |
|                    0                                                        |
|                                                                             |
|o9 : SpectralSequencePageMap                                                 |
|-----------------------------------------------------------------------------|
|          8                                                                  |
|-------- A  : {2, 1}                                                         |
|     |                                                                       |
|-yw2 |                                                                       |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                  12                         |
|------------------------------------------------ A   : {1, 1}                |
|     0       0      0       0        0       |                               |
|+y2w -z3+yw2 0      0       0        0       |                               |
|     0       -yz+xw -y3+x2z -xz2+y2w -z3+yw2 |                               |
|                                                                             |
|                                                                             |
|2}                                                                           |
+-----------------------------------------------------------------------------+
|i10 : F^0                                                                    |
|                                                                             |
|      +------+------+------+------+                                          |
|      | 2    | 8    | 8    | 2    |                                          |
|o10 = |A     |A     |A     |A     |                                          |
|      |      |      |      |      |                                          |
|      |{0, 2}|{1, 2}|{2, 2}|{3, 2}|                                          |
|      +------+------+------+------+                                          |
|      | 3    | 12   | 12   | 3    |                                          |
|      |A     |A     |A     |A     |                                          |
|      |      |      |      |      |                                          |
|      |{0, 1}|{1, 1}|{2, 1}|{3, 1}|                                          |
|      +------+------+------+------+                                          |
|      | 1    | 4    | 4    | 1    |                                          |
|      |A     |A     |A     |A     |                                          |
|      |      |      |      |      |                                          |
|      |{0, 0}|{1, 0}|{2, 0}|{3, 0}|                                          |
|      +------+------+------+------+                                          |
|                                                                             |
|o10 : SpectralSequencePage                                                   |
+-----------------------------------------------------------------------------+

The first pages take the form:

+-----------------------------------------------------------------------------+
|i11 : E^1                                                                    |
|                                                                             |
|      +----------------------------------------+-----------------------------|
|o11 = |cokernel | yz-xw z3-yw2 xz2-y2w y3-x2z ||cokernel {2} | yz-xw 0     0 |
|      |                                        |         {2} | 0     yz-xw 0 |
|      |{0, 0}                                  |         {2} | 0     0     yz|
|      |                                        |                             |
|      |                                        |{1, 0}                       |
|      +----------------------------------------+-----------------------------|
|                                                                             |
|o11 : SpectralSequencePage                                                   |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------+-----|
|    z3-yw2 xz2-y2w y3-x2z 0      0       0      0      0       0      ||coker|
|    0      0       0      z3-yw2 xz2-y2w y3-x2z 0      0       0      ||     |
|-xw 0      0       0      0      0       0      z3-yw2 xz2-y2w y3-x2z ||     |
|                                                                       |{2, 0|
|                                                                       |     |
|-----------------------------------------------------------------------+-----|
|-----------------------------------------------------------------------------|
|-------------------------------------------------------------------+         |
|nel {3} | yz-xw 0     z3-yw2 xz2-y2w y3-x2z 0      0       0      ||         |
|    {3} | 0     yz-xw 0      0       0      z3-yw2 xz2-y2w y3-x2z ||         |
|                                                                   |         |
|}                                                                  |         |
|                                                                   |         |
|-------------------------------------------------------------------+         |
+-----------------------------------------------------------------------------+
|i12 : F^1                                                                    |
|                                                                             |
|      +------------------------------+---------------------------------------|
|o12 = |cokernel | z2-yw yz-xw y2-xz ||cokernel {2} | z2-yw yz-xw y2-xz 0     |
|      |                              |         {3} | 0     0     0     z2-yw |
|      |{0, 0}                        |         {3} | 0     0     0     0     |
|      |                              |         {3} | 0     0     0     0     |
|      |                              |                                       |
|      |                              |{1, 0}                                 |
|      +------------------------------+---------------------------------------|
|                                                                             |
|o12 : SpectralSequencePage                                                   |
|-----------------------------------------------------------------------------|
|-------------------------------------------------+---------------------------|
|0     0     0     0     0     0     0     0     ||cokernel {4} | z2-yw yz-xw |
|yz-xw y2-xz 0     0     0     0     0     0     ||         {4} | 0     0     |
|0     0     z2-yw yz-xw y2-xz 0     0     0     ||         {4} | 0     0     |
|0     0     0     0     0     z2-yw yz-xw y2-xz ||         {4} | 0     0     |
|                                                 |                           |
|                                                 |{2, 0}                     |
|-------------------------------------------------+---------------------------|
|-----------------------------------------------------------------------------|
|-------------------------------------------------------------+---------------|
|y2-xz 0     0     0     0     0     0     0     0     0     ||cokernel {5} | |
|0     z2-yw yz-xw y2-xz 0     0     0     0     0     0     ||               |
|0     0     0     0     z2-yw yz-xw y2-xz 0     0     0     ||{3, 0}         |
|0     0     0     0     0     0     0     z2-yw yz-xw y2-xz ||               |
|                                                             |               |
|                                                             |               |
|-------------------------------------------------------------+---------------|
|-----------------------------------------------------------------------------|
|-------------------+                                                         |
|z2-yw yz-xw y2-xz ||                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|-------------------+                                                         |
+-----------------------------------------------------------------------------+

The second pages take the form:

+-----------------------------------------------------------------------------+
|i13 : E^2                                                                    |
|                                                                             |
|      +------------------------------------------------------+---------------|
|o13 = |cokernel | z2-yw yz-xw y2-xz xw2-yw2 xyw-xzw x2z-x2w ||cokernel {2} | |
|      |                                                      |               |
|      |{0, 0}                                                |{1, 0}         |
|      +------------------------------------------------------+---------------|
|                                                                             |
|o13 : SpectralSequencePage                                                   |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------+                 |
|z2-yw yz-xw y2-xz xw2-yw2 xzw-yw2 xyw-yw2 x2w-yw2 x2z-yw2 ||                 |
|                                                           |                 |
|                                                           |                 |
|-----------------------------------------------------------+                 |
+-----------------------------------------------------------------------------+
|i14 : F^2                                                                    |
|                                                                             |
|      +------------------------------------------------------+---------------|
|o14 = |cokernel | z2-yw yz-xw y2-xz xw2-yw2 xyw-xzw x2z-x2w ||cokernel {2} | |
|      |                                                      |               |
|      |{0, 0}                                                |{1, 0}         |
|      +------------------------------------------------------+---------------|
|                                                                             |
|o14 : SpectralSequencePage                                                   |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------+                 |
|z2-yw yz-xw y2-xz xw2-yw2 xzw-yw2 xyw-yw2 x2w-yw2 x2z-yw2 ||                 |
|                                                           |                 |
|                                                           |                 |
|-----------------------------------------------------------+                 |
+-----------------------------------------------------------------------------+

Observe that $E^2$ and $F^2$ are equal as they should.

See also
========

  * Filtrations and tensor product complexes
  * Filtrations and homomorphism complexes
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2064:0.

basis(List,SpectralSequencePage) -- generators of a particular degree
*********************************************************************

  * Function: basis (Macaulay2Doc),
  * Usage:
        B = basis(L, E)
  * Inputs:
      * L, a list (Macaulay2Doc),
      * E, a spectral sequence page,
  * Optional inputs (Macaulay2Doc),:
      * Degree (Macaulay2Doc), => ..., default value null,
      * Limit (Macaulay2Doc), => ..., default value infinity,
      * SourceRing (Macaulay2Doc), => ..., default value null,
      * Strategy (Macaulay2Doc), => ..., default value null,
      * Truncate (Macaulay2Doc), => ..., default value false,
      * Variables (Macaulay2Doc), => ..., default value null,
  * Outputs:
      * B, a matrix (Macaulay2Doc), Note!!  The output should
        actually be a page!!;

Description
===========

Returns generators for the requested (multi)degree of the spectral sequence
page.  It is designed to extend the function basis (Macaulay2Doc),
which can be applied to modules, for instance.

As a specific example consider the filtered complex $K$ below, obtained by
multiplying the minimal free resolution of the rational quartic space curve by
successive powers of the irrelevant ideal.

+----------------------------------------------------+
|i1 : B = QQ[a..d];                                  |
+----------------------------------------------------+
|i2 : J = ideal vars B;                              |
|                                                    |
|o2 : Ideal of B                                     |
+----------------------------------------------------+
|i3 : C = complete res monomialCurveIdeal(B,{1,3,4});|
+----------------------------------------------------+
|i4 : K = filteredComplex(J,C,4);                    |
+----------------------------------------------------+

We compute the degree $0$ piece of the $E^3$ page below.

+-----------------------------------------------------------------------------+
|i5 : E = prune spectralSequence K;                                           |
+-----------------------------------------------------------------------------+
|i6 : E^3                                                                     |
|                                                                             |
|     +-----------------------------------------------------------------------|
|o6 = |cokernel {4} | -d -b -d -c 0  0  -c 0  0  0  -d 0  0  0  0  -d -c 0  0 |
|     |         {4} | c  a  0  0  0  -d 0  -b 0  -d 0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  b  a  c  0  0  0  -d 0  0  -d 0  -d 0  0  0  0  0 |
|     |         {4} | 0  0  0  0  -d c  b  a  0  0  0  0  -d 0  -d 0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  c  b  a  0  0  0  0  0  0  0  -d|
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  b  a  0  0  0  0  c  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  d  c  b  a  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -d c |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |                                                                       |
|     |{-4, 4}                                                                |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 3}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 2}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 1}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 0}                                                                |
|     +-----------------------------------------------------------------------|
|                                                                             |
|o6 : SpectralSequencePage                                                    |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  -d 0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  -d 0  0  0  -d 0  0  0  0  -d 0  0  0  0  -d 0  0  0  0  0  0  0|
| -d 0  0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  -d 0  0  0  0  -d 0  0  0|
| 0  0  -d 0  0  -d 0  0  0  0  0  -d 0  0  0  0  -d 0  0  0  0  0  0  0  0  -|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| b  a  0  0  0  0  -d 0  0  0  0  0  -d 0  0  0  0  0  0  0  0  -d 0  0  0  0|
| 0  0  c  b  a  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  -d 0  0  0  0  0|
| 0  0  0  0  0  b  a  0  0  0  0  0  0  0  0  0  0  0  0  c  0  0  0  -d 0  0|
| 0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -d c  b  a  0  -d 0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  d  c  b|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|d 0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  -d 0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  -d 0  0  0  -d 0  0  0  0  0  0  -d 0  0  0  -d 0  0  -d 0  0  0  0  -d |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  -d 0  0  0  0  |
|  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  c  b  a  -d 0  0  0  -d 0  0  0  0  0  0  -d 0  0  0  0  0  0  0  -d 0  |
|  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  c  b  a  -d 0  0  0  0  0  0  -d 0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  c  b  a  -d 0  0  -d 0  0  0  0  -d 0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  0  0  0  0  -d 0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  d  c  b  a  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|----------------------------+------------------------------------------------|
|0  0  0  0  0  0  0  0  0  ||0                                               |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||{-3, 4}                                         |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  -d 0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  -d 0  0  0  -d 0  0  0  ||                                                |
|0  0  0  0  -d 0  0  0  -d ||                                                |
|-d 0  0  0  0  0  0  -d 0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|c  b  a  -d 0  0  0  0  0  ||                                                |
|0  0  0  c  b  a  -d 0  0  ||                                                |
|0  0  0  0  0  0  c  b  a  ||                                                |
|                            |                                                |
|                            |                                                |
|----------------------------+------------------------------------------------|
|                            |cokernel {3} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                            |         {3} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0|
|                            |         {3} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0|
|                            |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0|
|                            |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d|
|                            |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                            |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                            |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                            |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                            |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                            |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                            |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                            |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                            |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                            |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                            |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                            |                                                |
|                            |{-3, 3}                                         |
|----------------------------+------------------------------------------------|
|                            |0                                               |
|                            |                                                |
|                            |{-3, 2}                                         |
|                            |                                                |
|                            |                                                |
|                            |                                                |
|                            |                                                |
|                            |                                                |
|                            |                                                |
|                            |                                                |
|                            |                                                |
|----------------------------+------------------------------------------------|
|                            |0                                               |
|                            |                                                |
|                            |{-3, 1}                                         |
|                            |                                                |
|                            |                                                |
|                            |                                                |
|----------------------------+------------------------------------------------|
|                            |0                                               |
|                            |                                                |
|                            |{-3, 0}                                         |
|----------------------------+------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-------------------+---------------------------------------------------------|
|                   |0                                                        |
|                   |                                                         |
|                   |{-2, 4}                                                  |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|-------------------+---------------------------------------------------------|
|0 0 0 0 0 0 0 0 0 ||0                                                        |
|0 0 0 0 0 0 0 0 0 ||                                                         |
|0 0 0 0 0 0 0 0 0 ||{-2, 3}                                                  |
|0 0 0 0 0 0 0 0 0 ||                                                         |
|0 0 0 0 0 0 0 0 0 ||                                                         |
|0 0 0 0 0 0 0 0 0 ||                                                         |
|0 0 0 0 0 0 0 0 0 ||                                                         |
|0 0 0 0 0 0 0 0 0 ||                                                         |
|0 0 0 0 0 0 0 0 0 ||                                                         |
|0 0 0 0 0 0 0 0 0 ||                                                         |
|0 0 0 0 0 0 0 0 0 ||                                                         |
|0 0 0 0 0 0 0 0 0 ||                                                         |
|0 0 0 0 0 0 0 0 0 ||                                                         |
|a 0 0 0 0 0 0 0 0 ||                                                         |
|0 d c b a 0 0 0 0 ||                                                         |
|0 0 0 0 0 d c b a ||                                                         |
|                   |                                                         |
|                   |                                                         |
|-------------------+---------------------------------------------------------|
|                   |cokernel {2} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|                   |         {2} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|                   |         {2} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 |
|                   |         {2} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 |
|                   |         {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 |
|                   |         {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d |
|                   |         {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|                   |         {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|                   |         {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|                   |                                                         |
|                   |{-2, 2}                                                  |
|-------------------+---------------------------------------------------------|
|                   |0                                                        |
|                   |                                                         |
|                   |{-2, 1}                                                  |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|-------------------+---------------------------------------------------------|
|                   |0                                                        |
|                   |                                                         |
|                   |{-2, 0}                                                  |
|-------------------+---------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-------------------------------+---------------------------------------------|
|                               |0                                            |
|                               |                                             |
|                               |{-1, 4}                                      |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|-------------------------------+---------------------------------------------|
|                               |0                                            |
|                               |                                             |
|                               |{-1, 3}                                      |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|-------------------------------+---------------------------------------------|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||cokernel {4} | d c b a 0 0 0 0 0 0 0 0 0 0 0 |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||         {4} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||         {4} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||         {4} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||         {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|c b a 0 0 0 0 0 0 0 0 0 0 0 0 ||         {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|0 0 0 d c b a 0 0 0 0 0 0 0 0 ||         {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|0 0 0 0 0 0 0 d c b a 0 0 0 0 ||         {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|0 0 0 0 0 0 0 0 0 0 0 d c b a ||                                             |
|                               |{-1, 2}                                      |
|                               |                                             |
|-------------------------------+---------------------------------------------|
|                               |cokernel {1} | d c b a 0 0 0 0 0 0 0 0 0 0 0 |
|                               |         {1} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 |
|                               |         {1} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 |
|                               |         {1} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b |
|                               |                                             |
|                               |{-1, 1}                                      |
|-------------------------------+---------------------------------------------|
|                               |0                                            |
|                               |                                             |
|                               |{-1, 0}                                      |
|-------------------------------+---------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------+----------------------------------------+|
|                                   |0                                       ||
|                                   |                                        ||
|                                   |{0, 4}                                  ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|-----------------------------------+----------------------------------------+|
|                                   |0                                       ||
|                                   |                                        ||
|                                   |{0, 3}                                  ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|-----------------------------------+----------------------------------------+|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||0                                       ||
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                                        ||
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||{0, 2}                                  ||
|a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                                        ||
|0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 ||                                        ||
|0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 ||                                        ||
|0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 ||                                        ||
|0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a ||                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|-----------------------------------+----------------------------------------+|
|0 |                                |cokernel {3} | d c b a 0 0 0 0 0 0 0 0 |||
|0 |                                |         {3} | 0 0 0 0 d c b a 0 0 0 0 |||
|0 |                                |         {3} | 0 0 0 0 0 0 0 0 d c b a |||
|a |                                |                                        ||
|                                   |{0, 1}                                  ||
|                                   |                                        ||
|-----------------------------------+----------------------------------------+|
|                                   |cokernel | d c b a |                    ||
|                                   |                                        ||
|                                   |{0, 0}                                  ||
|-----------------------------------+----------------------------------------+|
+-----------------------------------------------------------------------------+
|i7 : basis(0,E^3)                                                            |
|                                                                             |
|     +------+                                                                |
|o7 = || 1 | |                                                                |
|     |      |                                                                |
|     |{0, 0}|                                                                |
|     +------+                                                                |
|                                                                             |
|o7 : Page                                                                    |
+-----------------------------------------------------------------------------+

See also
========

  * basis (Macaulay2Doc) -- basis or generating set of all or part
    of a ring, ideal or module

Ways to use this method:
========================

  * basis(List,SpectralSequencePage)
    -- generators of a particular
    degree
  * "basis(ZZ,SpectralSequencePage)"
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:3027:0.

ChainComplex ** FilteredComplex -- filtered tensor product of complexes
***********************************************************************

  * Operator: ** (Macaulay2Doc),
  * Usage:
        KK = C ** K
        KK = K ** C
  * Inputs:
      * C, a chain complex (OldChainComplexes),
      * K, a filtered chain complex,
  * Outputs:
      * KK, a filtered chain complex,

Description
===========

Returns the two filtrations of the tensor product complex determined by the
double complex. The following example illustrates the syntax.

+-----------------------------------------------------------------------------+
|i1 : A = QQ[x,y];                                                            |
+-----------------------------------------------------------------------------+
|i2 : B = koszul vars A;                                                      |
+-----------------------------------------------------------------------------+
|i3 : C = koszul vars A;                                                      |
+-----------------------------------------------------------------------------+
|i4 : F' = (filteredComplex B) ** C                                           |
|                                                                             |
|o4 = -1 : image 0 <-- image 0 <-- image 0 <-- image 0 <-- image 0            |
|                                                                             |
|          0           1           2           3           4                  |
|                                                                             |
|     0 : image | 1 | <-- image {1} | 1 0 0 0 | <-- image {2} | 1 0 0 0 0 0 | |
|                               {1} | 0 1 0 0 |           {2} | 0 0 0 0 0 0 | |
|         0                     {1} | 0 0 0 0 |           {2} | 0 0 0 0 0 0 | |
|                               {1} | 0 0 0 0 |           {2} | 0 0 0 0 0 0 | |
|                                                         {2} | 0 0 0 0 0 0 | |
|                         1                               {2} | 0 0 0 0 0 0 | |
|                                                                             |
|                                                   2                         |
|                                                                             |
|     1 : image | 1 | <-- image {1} | 1 0 0 0 | <-- image {2} | 1 0 0 0 0 0 | |
|                               {1} | 0 1 0 0 |           {2} | 0 1 0 0 0 0 | |
|         0                     {1} | 0 0 1 0 |           {2} | 0 0 1 0 0 0 | |
|                               {1} | 0 0 0 1 |           {2} | 0 0 0 1 0 0 | |
|                                                         {2} | 0 0 0 0 1 0 | |
|                         1                               {2} | 0 0 0 0 0 0 | |
|                                                                             |
|                                                   2                         |
|                                                                             |
|          1      4      6      4      1                                      |
|     2 : A  <-- A  <-- A  <-- A  <-- A                                       |
|                                                                             |
|         0      1      2      3      4                                       |
|                                                                             |
|o4 : FilteredComplex                                                         |
|-----------------------------------------------------------------------------|
|<-- image 0 <-- image 0                                                      |
|                                                                             |
|    3           4                                                            |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|<-- image {3} | 1 0 0 0 | <-- image 0                                        |
|          {3} | 0 1 0 0 |                                                    |
|          {3} | 0 0 0 0 |     4                                              |
|          {3} | 0 0 0 0 |                                                    |
|                                                                             |
|    3                                                                        |
+-----------------------------------------------------------------------------+
|i5 : F'' = B ** (filteredComplex C)                                          |
|                                                                             |
|o5 = -1 : image 0 <-- image 0 <-- image 0 <-- image 0 <-- image 0            |
|                                                                             |
|          0           1           2           3           4                  |
|                                                                             |
|     0 : image | 1 | <-- image {1} | 0 0 0 0 | <-- image {2} | 0 0 0 0 0 0 | |
|                               {1} | 0 0 0 0 |           {2} | 0 0 0 0 0 0 | |
|         0                     {1} | 0 0 1 0 |           {2} | 0 0 0 0 0 0 | |
|                               {1} | 0 0 0 1 |           {2} | 0 0 0 0 0 0 | |
|                                                         {2} | 0 0 0 0 0 0 | |
|                         1                               {2} | 0 0 0 0 0 1 | |
|                                                                             |
|                                                   2                         |
|                                                                             |
|     1 : image | 1 | <-- image {1} | 1 0 0 0 | <-- image {2} | 0 0 0 0 0 0 | |
|                               {1} | 0 1 0 0 |           {2} | 0 1 0 0 0 0 | |
|         0                     {1} | 0 0 1 0 |           {2} | 0 0 1 0 0 0 | |
|                               {1} | 0 0 0 1 |           {2} | 0 0 0 1 0 0 | |
|                                                         {2} | 0 0 0 0 1 0 | |
|                         1                               {2} | 0 0 0 0 0 1 | |
|                                                                             |
|                                                   2                         |
|                                                                             |
|          1      4      6      4      1                                      |
|     2 : A  <-- A  <-- A  <-- A  <-- A                                       |
|                                                                             |
|         0      1      2      3      4                                       |
|                                                                             |
|o5 : FilteredComplex                                                         |
|-----------------------------------------------------------------------------|
|<-- image 0 <-- image 0                                                      |
|                                                                             |
|    3           4                                                            |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|<-- image {3} | 0 0 0 0 | <-- image 0                                        |
|          {3} | 0 0 0 0 |                                                    |
|          {3} | 0 0 1 0 |     4                                              |
|          {3} | 0 0 0 1 |                                                    |
|                                                                             |
|    3                                                                        |
+-----------------------------------------------------------------------------+

See also
========

  * Filtrations and tensor product complexes

Ways to use this method:
========================

  * ChainComplex ** FilteredComplex,
    -- filtered tensor product of complexes
  * "FilteredComplex ** ChainComplex"
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:3587:0.

chainComplex(FilteredComplex) -- the ambient chain complex of a filtered complex
********************************************************************************

  * Function: chainComplex (OldChainComplexes),
  * Usage:
        C = chainComplex K
  * Inputs:
      * K, a filtered chain complex,
  * Outputs:
      * C, a chain complex (OldChainComplexes),

Description
===========

Returns the ambient chain complex of the filtered complex.

+---------------------------+
|i1 : A = QQ[x,y];          |
+---------------------------+
|i2 : C = koszul vars A     |
|                           |
|      1      2      1      |
|o2 = A  <-- A  <-- A       |
|                           |
|     0      1      2       |
|                           |
|o2 : ChainComplex          |
+---------------------------+
|i3 : K = filteredComplex C;|
+---------------------------+
|i4 : chainComplex K        |
|                           |
|      1      2      1      |
|o4 = A  <-- A  <-- A       |
|                           |
|     0      1      2       |
|                           |
|o4 : ChainComplex          |
+---------------------------+
|i5 : K_infinity            |
|                           |
|      1      2      1      |
|o5 = A  <-- A  <-- A       |
|                           |
|     0      1      2       |
|                           |
|o5 : ChainComplex          |
+---------------------------+

See also
========

  * FilteredComplex _ ZZ -- the filtered pieces
  * FilteredComplex _ InfiniteNumber -- the
    filtered pieces
  * FilteredComplex ^ ZZ -- the filtered pieces
  * FilteredComplex ^ InfiniteNumber -- the
    filtered pieces

Ways to use this method:
========================

  * chainComplex(FilteredComplex), --
    the ambient chain complex of a filtered complex
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:3083:0.

chainComplex(SpectralSequence) -- the underlying chain complex of a Spectral Sequence
*************************************************************************************

  * Function: chainComplex (OldChainComplexes),
  * Usage:
        K = chainComplex E
  * Inputs:
      * E, a spectral sequence,
  * Outputs:
      * K, a chain complex (OldChainComplexes),

Description
===========

Returns the underlying chain complex of a spectral sequence.

+---------------------------+
|i1 : A = QQ[x,y];          |
+---------------------------+
|i2 : C = koszul vars A     |
|                           |
|      1      2      1      |
|o2 = A  <-- A  <-- A       |
|                           |
|     0      1      2       |
|                           |
|o2 : ChainComplex          |
+---------------------------+
|i3 : K = filteredComplex C;|
+---------------------------+
|i4 : E = spectralSequence K|
|                           |
|o4 = E                     |
|                           |
|o4 : SpectralSequence      |
+---------------------------+
|i5 : chainComplex E        |
|                           |
|      1      2      1      |
|o5 = A  <-- A  <-- A       |
|                           |
|     0      1      2       |
|                           |
|o5 : ChainComplex          |
+---------------------------+

Ways to use this method:
========================

  * chainComplex(SpectralSequence),
    -- the underlying chain complex of a Spectral Sequence
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:3238:0.

Computing the Serre Spectral Sequence associated to a Hopf Fibration
********************************************************************

We compute the Serre Spectral Sequence associated to the Hopf Fibration $S^1
\rightarrow S^3 \rightarrow S^2$. This example is made possible by the minimal
triangulation of this fibration given in the paper "A minimal triangulation of
the Hopf map and its application" by K.V. Madahar and K.S Sarkaria. Geom
Dedicata, 2000.

We first make the relevant simplicial complexes described on page 110 of the
paper.  The simplicial complex $S3$ below is a triangulation of $S^3$.

+-----------------------------------------------------------------------------+
|i1 : B = QQ[a_0..a_2,b_0..b_2,c_0..c_2,d_0..d_2];                            |
+-----------------------------------------------------------------------------+
|i2 : l1 = {a_0*b_0*b_1*c_1,a_0*b_0*c_0*c_1,a_0*a_1*b_1*c_1,b_0*b_1*c_1*d_1,b_|
|-----------------------------------------------------------------------------|
|0*c_0*c_1*d_2,a_0*a_1*c_1*d_2,a_0*c_0*c_1*d_2,b_0*c_1*d_1*d_2};              |
+-----------------------------------------------------------------------------+
|i3 : l2 = {b_1*c_1*c_2*a_2,b_1*c_1*a_1*a_2,b_1*b_2*c_2*a_2,c_1*c_2*a_2*d_1,c_|
|-----------------------------------------------------------------------------|
|1*a_1*a_2*d_2,b_1*b_2*a_2*d_2,b_1*a_1*a_2*d_2,c_1*a_2*d_1*d_2};              |
+-----------------------------------------------------------------------------+
|i4 : l3 = {c_2*a_2*a_0*b_0,c_2*a_2*b_2*b_0,c_2*c_0*a_0*b_0,a_2*a_0*b_0*d_1,a_|
|-----------------------------------------------------------------------------|
|2*b_2*b_0*d_2,c_2*c_0*b_0*d_2,c_2*b_2*b_0*d_2,a_2*b_0*d_1*d_2};              |
+-----------------------------------------------------------------------------+
|i5 : l4 = {a_0*b_0*b_1*d_1,a_0*b_1*d_0*d_1,b_1*c_1*c_2*d_1,b_1*c_2*d_0*d_1,a_|
|-----------------------------------------------------------------------------|
|0*a_2*c_2*d_1,a_0*c_2*d_0*d_1};                                              |
+-----------------------------------------------------------------------------+
|i6 : l5 = {a_0*b_1*d_0*d_2,a_0*a_1*b_1*d_2,b_1*c_2*d_0*d_2,b_1*b_2*c_2*d_2,a_|
|-----------------------------------------------------------------------------|
|0*c_2*d_0*d_2,a_0*c_0*c_2*d_2};                                              |
+-----------------------------------------------------------------------------+
|i7 : S3 = simplicialComplex(join(l1,l2,l3,l4,l5));                           |
+-----------------------------------------------------------------------------+

We identify the two sphere $S^2$ with the simplicial complex $S2$ defined by
the facets $\{abc, abd, bcd, acd \}$.  The Hopf fibration $S^1 \rightarrow S^3
\rightarrow S^2$ is then realized by the simplicial map $p: S3 \rightarrow S2$
defined by $a_i \mapsto a$, $b_i \mapsto b$, $c_i \mapsto c$, and $d_i \mapsto
d$.

We now explain how to construct the filtration of $S3$ obtained by considering
the $k$-skeletons of this fibration.

The simplicial complex $F1S3$ below is the subsimplicial complex of $S3$
obtained by considering the inverse images of the $1$-dimensional faces of the
simplicial complex $S2$. We first describe the simplicial complex $F1S3$ in
pieces.

For example, to compute $f1l1$ below, we observe that the inverse image of $ab$
under $p$ is $a_0b_0b_1, a_0a_1b_1$ etc. All of these inverse images have been
computed by hand previously.

+-----------------------------------------------------------------------------+
|i8 : f1l1 = {a_0*b_0*b_1,a_0*a_1*b_1,a_0*c_0*c_1,a_0*a_1*c_1,a_0*a_1*d_2,d_1*|
|-----------------------------------------------------------------------------|
|d_2,b_0*b_1*c_1,b_0*c_0*c_1,b_0*b_1*d_1,b_0*d_1*d_2,c_1*d_1*d_2,c_0*c_1*d_2};|
+-----------------------------------------------------------------------------+
|i9 : f1l2 = {b_1*a_1*a_2,b_1*b_2*a_2,c_1*c_2*a_2,c_1*a_1*a_2,a_1*a_2*d_2,a_2*|
|-----------------------------------------------------------------------------|
|d_1*d_2,b_1*c_1*c_2,b_1*b_2*c_2,b_1*b_2*d_2,d_1*d_2,c_1*d_1*d_2,c_1*c_2*d_1};|
+-----------------------------------------------------------------------------+
|i10 : f1l3 = {a_2*a_0*b_0,a_2*b_2*b_0,                                       |
|-----------------------------------------------------------------------------|
|c_2*a_2*a_0,c_2*c_0*a_0,a_2*a_0*d_1,a_2*d_1*d_2,b_2*b_0*c_2,c_2*c_0*b_0,b_2*b|
|-----------------------------------------------------------------------------|
|_0*d_2,b_0*d_1*d_2,c_2*c_0*d_2,d_1*d_2};                                     |
+-----------------------------------------------------------------------------+
|i11 : f1l4 = {a_0*b_0*b_1,a_0*a_2,a_0*a_2*c_2,c_1*c_2,a_0*d_0*d_1,a_0*a_2*d_1|
|                                                                             |
|o11 = {a b b , a a , a a c , c c , a d d , a a d , b c c , b b , b b d ,     |
|        0 0 1   0 2   0 2 2   1 2   0 0 1   0 2 1   1 1 2   0 1   0 1 1      |
|      -----------------------------------------------------------------------|
|      b d d , c c d , c d d }                                                |
|       1 0 1   1 2 1   2 0 1                                                 |
|                                                                             |
|o11 : List                                                                   |
|-----------------------------------------------------------------------------|
|,b_1*c_1*c_2,b_0*b_1,b_0*b_1*d_1,b_1*d_0*d_1,c_1*c_2*d_1,c_2*d_0*d_1}        |
+-----------------------------------------------------------------------------+
|i12 : f1l5 = {a_0*a_1*b_1,b_1*b_2,a_0*c_0*c_2,a_0*a_1,a_0*d_0*d_2,a_0*a_1*d_2|
|-----------------------------------------------------------------------------|
|,b_1*b_2*c_2,c_0*c_2,b_1*d_0*d_2,b_1*b_2*d_2,c_2*d_0*d_2,c_0*c_2*d_2};       |
+-----------------------------------------------------------------------------+
|i13 : F1S3 = simplicialComplex(join(f1l1,f1l2,f1l3,f1l4,f1l5));              |
+-----------------------------------------------------------------------------+

The simplicial complex $F0S3$ below is the subsimplicial complex of $F1S3$
obtained by considering the inverse images of the $0$-dimensional faces of the
simplicial complex $S2$.  Again we describe this simplicial complex in pieces.

+---------------------------------------------------------------+
|i14 : f0l1 = {a_0*a_1,b_0*b_1,c_0*c_1,d_1*d_2};                |
+---------------------------------------------------------------+
|i15 : f0l2 = {a_1*a_2,b_1*b_2,c_1*c_2,d_1*d_2};                |
+---------------------------------------------------------------+
|i16 : f0l3 = {a_0*a_2,b_0*b_2,c_0*c_2,d_1*d_2};                |
+---------------------------------------------------------------+
|i17 : f0l4 = {a_0*a_2,b_0*b_1,c_1*c_2,d_0*d_1};                |
+---------------------------------------------------------------+
|i18 : f0l5 = {a_0*a_1,b_1*b_2,c_0*c_2,d_0*d_2};                |
+---------------------------------------------------------------+
|i19 : F0S3 = simplicialComplex(join(f0l1,f0l2,f0l3,f0l4,f0l5));|
+---------------------------------------------------------------+

The simplicial complex $S3$ is obtained by considering the inverse images of
the $2$ dimensional faces of $S2$.

To compute a simplicial version of the Serre spectral sequence for the $S^1
\rightarrow S^3 \rightarrow S^2$ correctly, meaning that the spectral sequence
takes the form $E^2_{p,q} = H_p(S^2,H_q(S^1,QQ))$, we need to use non-reduced
homology.

+--------------------------------------------------------------------+
|i20 : K = filteredComplex({S3,F1S3,F0S3}, ReducedHomology => false);|
+--------------------------------------------------------------------+

We now compute the various pages of the spectral sequence. To make the output
intelligible we prune the spectral sequence.

+-----------------------------------+
|i21 : E = prune spectralSequence K;|
+-----------------------------------+
+----------------------------+
|i22 : E0 = E^0              |
|                            |
|      +------+------+------+|
|      |  12  |  36  |  36  ||
|o22 = |QQ    |QQ    |QQ    ||
|      |      |      |      ||
|      |{0, 1}|{1, 1}|{2, 1}||
|      +------+------+------+|
|      |  12  |  36  |  36  ||
|      |QQ    |QQ    |QQ    ||
|      |      |      |      ||
|      |{0, 0}|{1, 0}|{2, 0}||
|      +------+------+------+|
|                            |
|o22 : SpectralSequencePage  |
+----------------------------+

Here are the maps.

+-----------------------------------------------------------------------------+
|i23 : E0.dd                                                                  |
|                                                                             |
|o23 = {-1, 0} : 0 <----- 0 : {-1, 1}                                         |
|                     0                                                       |
|                                                                             |
|      {-1, 1} : 0 <----- 0 : {-1, 2}                                         |
|                     0                                                       |
|                                                                             |
|      {-1, 2} : 0 <----- 0 : {-1, 3}                                         |
|                     0                                                       |
|                                                                             |
|      {-1, 3} : 0 <----- 0 : {-1, 4}                                         |
|                     0                                                       |
|                                                                             |
|      {2, -4} : 0 <----- 0 : {2, -3}                                         |
|                     0                                                       |
|                                                                             |
|      {2, -3} : 0 <----- 0 : {2, -2}                                         |
|                     0                                                       |
|                                                                             |
|      {2, -2} : 0 <----- 0 : {2, -1}                                         |
|                     0                                                       |
|                                                                             |
|                           36                                                |
|      {2, -1} : 0 <----- QQ   : {2, 0}                                       |
|                     0                                                       |
|                                                                             |
|                 36                                                          |
|      {2, 0} : QQ   <--------------------------------------------------------|
|                       | 0  0  0  0  0  0  0  0  1  1  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  -1 0  -1 0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  1  0  0  0  0  0  -1 0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  1  0  0  -1 0  0  0  0  0  0  0  0  0  0|
|                       | 1  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  1  1  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  1  0  0  -1 0  0  0  0  0  0  0|
|                       | 0  1  0  0  0  0  0  0  0  0  0  -1 0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  -1 -1 0  0  0  0|
|                       | 0  0  1  0  0  0  0  0  0  0  0  0  1  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  1  0  0|
|                       | 0  0  0  0  0  1  0  0  0  0  0  0  0  0  -1 0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  -1 0  0|
|                       | -1 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  0|
|                       | 0  -1 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1|
|                       | 0  0  -1 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  -1 0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  -1 0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -1 0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  -1 0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                                                                             |
|      {1, -3} : 0 <----- 0 : {1, -2}                                         |
|                     0                                                       |
|                                                                             |
|      {1, -2} : 0 <----- 0 : {1, -1}                                         |
|                     0                                                       |
|                                                                             |
|                           36                                                |
|      {1, -1} : 0 <----- QQ   : {1, 0}                                       |
|                     0                                                       |
|                                                                             |
|                 36                                                          |
|      {1, 0} : QQ   <--------------------------------------------------------|
|                       | 0  0  0  1  0  0  -1 0  0  0  0  0  0  0  0  0  0  0|
|                       | 1  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  -1 -1 0  0  0  0  0  0  0  0  0|
|                       | 0  1  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  1  0  0  0  1  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  -1 -1 0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  1  0  0  0  1  0  0  0  0  0  0  0  0|
|                       | 0  0  1  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0|
|                       | -1 0  0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0|
|                       | 0  -1 0  0  0  0  0  0  0  0  0  0  1  0  0  0  0  0|
|                       | 0  0  -1 0  0  0  0  0  0  0  0  0  0  1  0  0  0  0|
|                       | 0  0  0  -1 0  0  0  0  0  0  0  0  0  0  -1 0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  -1 0  0  0  -1 0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  1  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  -1 0  0  0  -1 0|
|                       | 0  0  0  0  -1 0  0  0  0  0  0  0  0  0  0  0  1  0|
|                       | 0  0  0  0  0  -1 0  0  0  0  0  0  0  0  0  0  0  -|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  -1 0  0  0  1|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                                                                             |
|                 36                                                          |
|      {1, 1} : QQ   <----- 0 : {1, 2}                                        |
|                       0                                                     |
|                                                                             |
|      {0, -2} : 0 <----- 0 : {0, -1}                                         |
|                     0                                                       |
|                                                                             |
|                           12                                                |
|      {0, -1} : 0 <----- QQ   : {0, 0}                                       |
|                     0                                                       |
|                                                                             |
|                 12                                                12        |
|      {0, 0} : QQ   <------------------------------------------- QQ   : {0, 1|
|                       | 1  1  0  0  0  0  0  0  0  0  0  0  |               |
|                       | -1 0  1  0  0  0  0  0  0  0  0  0  |               |
|                       | 0  -1 -1 0  0  0  0  0  0  0  0  0  |               |
|                       | 0  0  0  1  1  0  0  0  0  0  0  0  |               |
|                       | 0  0  0  -1 0  1  0  0  0  0  0  0  |               |
|                       | 0  0  0  0  -1 -1 0  0  0  0  0  0  |               |
|                       | 0  0  0  0  0  0  1  1  0  0  0  0  |               |
|                       | 0  0  0  0  0  0  -1 0  1  0  0  0  |               |
|                       | 0  0  0  0  0  0  0  -1 -1 0  0  0  |               |
|                       | 0  0  0  0  0  0  0  0  0  1  1  0  |               |
|                       | 0  0  0  0  0  0  0  0  0  -1 0  1  |               |
|                       | 0  0  0  0  0  0  0  0  0  0  -1 -1 |               |
|                                                                             |
|                 12                                                          |
|      {0, 1} : QQ   <----- 0 : {0, 2}                                        |
|                       0                                                     |
|                                                                             |
|      {0, 2} : 0 <----- 0 : {0, 3}                                           |
|                    0                                                        |
|                                                                             |
|      {-1, -1} : 0 <----- 0 : {-1, 0}                                        |
|                      0                                                      |
|                                                                             |
|o23 : SpectralSequencePageMap                                                |
|-----------------------------------------------------------------------------|
|                                                              36             |
|----------------------------------------------------------- QQ   : {2, 1}    |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  -1 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  -1 -1 0  0  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  0  -1 0  -1 0  0  0  0  0  0  0  0  0  0  0  |                    |
|1 0  0  0  0  0  -1 0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  1  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  1  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  -1 1  0  0  0  0  0  0  0  0  0  |                    |
|  -1 0  0  0  0  0  0  0  -1 0  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  0  0  0  0  -1 -1 0  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  0  0  1  0  0  0  1  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  0  0  0  0  1  0  -1 0  0  0  0  |                    |
|  0  0  0  0  0  0  0  0  0  0  1  0  1  0  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  0  0  -1 0  0  0  0  0  -1 0  0  |                    |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  1  |                    |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  -1 0  |                    |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0  -1 |                    |
|  0  0  0  0  0  0  0  0  0  0  -1 0  0  0  -1 0  0  0  |                    |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                              36             |
|----------------------------------------------------------- QQ   : {1, 1}    |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|1 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  0  -1 -1 0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  1  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  1  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  1  0  0  0  0  -1 0  0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  1  0  0  1  0  0  0  0  0  0  0  0  0  0  0  |                    |
|  -1 0  0  0  0  0  0  0  0  -1 0  0  0  0  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  1  0  1  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  0  0  0  -1 -1 0  0  0  0  0  0  |                    |
|  0  -1 0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  0  1  0  0  1  0  0  0  0  0  0  |                    |
|  0  0  -1 0  0  0  0  -1 0  0  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  -1 0  0  0  0  -1 0  0  0  0  0  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  0  0  0  0  0  1  1  0  0  0  0  |                    |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  -1 0  0  |                    |
|  0  0  0  0  0  0  0  0  0  0  0  0  -1 0  0  1  0  0  |                    |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -1 -1 |                    |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -1 0  1  0  |                    |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  -1 0  0  0  1  |                    |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|}                                                                            |
+-----------------------------------------------------------------------------+

Now try the $E^1$ page.

+----------------------------+
|i24 : E1 = E^1              |
|                            |
|      +------+------+------+|
|      |  4   |  6   |  4   ||
|o24 = |QQ    |QQ    |QQ    ||
|      |      |      |      ||
|      |{0, 1}|{1, 1}|{2, 1}||
|      +------+------+------+|
|      |  4   |  6   |  4   ||
|      |QQ    |QQ    |QQ    ||
|      |      |      |      ||
|      |{0, 0}|{1, 0}|{2, 0}||
|      +------+------+------+|
|                            |
|o24 : SpectralSequencePage  |
+----------------------------+

Here are the maps.

+----------------------------------------------------------+
|i25 : E1.dd                                               |
|                                                          |
|o25 = {-2, 1} : 0 <----- 0 : {-1, 1}                      |
|                     0                                    |
|                                                          |
|      {-2, 2} : 0 <----- 0 : {-1, 2}                      |
|                     0                                    |
|                                                          |
|      {-2, 3} : 0 <----- 0 : {-1, 3}                      |
|                     0                                    |
|                                                          |
|      {-2, 4} : 0 <----- 0 : {-1, 4}                      |
|                     0                                    |
|                                                          |
|      {1, -3} : 0 <----- 0 : {2, -3}                      |
|                     0                                    |
|                                                          |
|      {1, -2} : 0 <----- 0 : {2, -2}                      |
|                     0                                    |
|                                                          |
|      {1, -1} : 0 <----- 0 : {2, -1}                      |
|                     0                                    |
|                                                          |
|                 6                        4               |
|      {1, 0} : QQ  <------------------- QQ  : {2, 0}      |
|                      | -1 -1 0  0  |                     |
|                      | 1  0  -1 0  |                     |
|                      | 0  1  1  0  |                     |
|                      | -1 0  0  -1 |                     |
|                      | 0  -1 0  1  |                     |
|                      | 0  0  -1 -1 |                     |
|                                                          |
|                 6                      4                 |
|      {1, 1} : QQ  <----------------- QQ  : {2, 1}        |
|                      | 1 -1 0 0  |                       |
|                      | 0 1  1 0  |                       |
|                      | 1 0  1 0  |                       |
|                      | 0 -1 0 -1 |                       |
|                      | 1 0  0 1  |                       |
|                      | 0 0  1 -1 |                       |
|                                                          |
|      {0, -2} : 0 <----- 0 : {1, -2}                      |
|                     0                                    |
|                                                          |
|      {0, -1} : 0 <----- 0 : {1, -1}                      |
|                     0                                    |
|                                                          |
|                 4                              6         |
|      {0, 0} : QQ  <------------------------- QQ  : {1, 0}|
|                      | 1  1  1  0  0  0  |               |
|                      | -1 0  0  1  1  0  |               |
|                      | 0  -1 0  -1 0  1  |               |
|                      | 0  0  -1 0  -1 -1 |               |
|                                                          |
|                 4                            6           |
|      {0, 1} : QQ  <----------------------- QQ  : {1, 1}  |
|                      | 1  1  -1 0  0 0 |                 |
|                      | -1 0  0  1  1 0 |                 |
|                      | 0  -1 0  -1 0 1 |                 |
|                      | 0  0  -1 0  1 1 |                 |
|                                                          |
|      {0, 2} : 0 <----- 0 : {1, 2}                        |
|                    0                                     |
|                                                          |
|      {-1, -1} : 0 <----- 0 : {0, -1}                     |
|                      0                                   |
|                                                          |
|                           4                              |
|      {-1, 0} : 0 <----- QQ  : {0, 0}                     |
|                     0                                    |
|                                                          |
|                           4                              |
|      {-1, 1} : 0 <----- QQ  : {0, 1}                     |
|                     0                                    |
|                                                          |
|      {-1, 2} : 0 <----- 0 : {0, 2}                       |
|                     0                                    |
|                                                          |
|      {-1, 3} : 0 <----- 0 : {0, 3}                       |
|                     0                                    |
|                                                          |
|      {-2, 0} : 0 <----- 0 : {-1, 0}                      |
|                     0                                    |
|                                                          |
|o25 : SpectralSequencePageMap                             |
+----------------------------------------------------------+

Now try the $E^2$ page.

+----------------------------+
|i26 : E2 = E^2              |
|                            |
|      +------+------+------+|
|      |  1   |      |  1   ||
|o26 = |QQ    |0     |QQ    ||
|      |      |      |      ||
|      |{0, 1}|{1, 1}|{2, 1}||
|      +------+------+------+|
|      |  1   |      |  1   ||
|      |QQ    |0     |QQ    ||
|      |      |      |      ||
|      |{0, 0}|{1, 0}|{2, 0}||
|      +------+------+------+|
|                            |
|o26 : SpectralSequencePage  |
+----------------------------+

Here are the maps.

+------------------------------------------+
|i27 : E2.dd                               |
|                                          |
|o27 = {-3, 2} : 0 <----- 0 : {-1, 1}      |
|                     0                    |
|                                          |
|      {-3, 3} : 0 <----- 0 : {-1, 2}      |
|                     0                    |
|                                          |
|      {-3, 4} : 0 <----- 0 : {-1, 3}      |
|                     0                    |
|                                          |
|      {-3, 5} : 0 <----- 0 : {-1, 4}      |
|                     0                    |
|                                          |
|      {0, -2} : 0 <----- 0 : {2, -3}      |
|                     0                    |
|                                          |
|      {0, -1} : 0 <----- 0 : {2, -2}      |
|                     0                    |
|                                          |
|                 1                        |
|      {0, 0} : QQ  <----- 0 : {2, -1}     |
|                      0                   |
|                                          |
|                 1              1         |
|      {0, 1} : QQ  <--------- QQ  : {2, 0}|
|                      | 1 |               |
|                                          |
|                          1               |
|      {0, 2} : 0 <----- QQ  : {2, 1}      |
|                    0                     |
|                                          |
|      {-1, -1} : 0 <----- 0 : {1, -2}     |
|                      0                   |
|                                          |
|      {-1, 0} : 0 <----- 0 : {1, -1}      |
|                     0                    |
|                                          |
|      {-1, 1} : 0 <----- 0 : {1, 0}       |
|                     0                    |
|                                          |
|      {-1, 2} : 0 <----- 0 : {1, 1}       |
|                     0                    |
|                                          |
|      {-1, 3} : 0 <----- 0 : {1, 2}       |
|                     0                    |
|                                          |
|      {-2, 0} : 0 <----- 0 : {0, -1}      |
|                     0                    |
|                                          |
|                           1              |
|      {-2, 1} : 0 <----- QQ  : {0, 0}     |
|                     0                    |
|                                          |
|                           1              |
|      {-2, 2} : 0 <----- QQ  : {0, 1}     |
|                     0                    |
|                                          |
|      {-2, 3} : 0 <----- 0 : {0, 2}       |
|                     0                    |
|                                          |
|      {-2, 4} : 0 <----- 0 : {0, 3}       |
|                     0                    |
|                                          |
|      {-3, 1} : 0 <----- 0 : {-1, 0}      |
|                     0                    |
|                                          |
|o27 : SpectralSequencePageMap             |
+------------------------------------------+

Note that the modules on the $E^2$ page appear to have been computed correctly.
The statement of the Serre spectral sequence, see for example Theorem 1.3 p. 8
of Hatcher's Spectral Sequence book, asserts that $E^2_{p,q} =
H_p(S^2,H_q(S^1,QQ))$. This is exactly what we obtained above.  Also the maps
on the $E^2$ page also seem to be computed correctly as the spectral sequence
will abut to the homology of $S^3$.

+-------------------------------------+
|i28 : E3 = E^3                       |
|                                     |
|      +------+------+------+         |
|      |      |      |  1   |         |
|o28 = |0     |0     |QQ    |         |
|      |      |      |      |         |
|      |{0, 1}|{1, 1}|{2, 1}|         |
|      +------+------+------+         |
|      |  1   |      |      |         |
|      |QQ    |0     |0     |         |
|      |      |      |      |         |
|      |{0, 0}|{1, 0}|{2, 0}|         |
|      +------+------+------+         |
|                                     |
|o28 : SpectralSequencePage           |
+-------------------------------------+
|i29 : E3.dd                          |
|                                     |
|o29 = {-4, 3} : 0 <----- 0 : {-1, 1} |
|                     0               |
|                                     |
|      {-4, 4} : 0 <----- 0 : {-1, 2} |
|                     0               |
|                                     |
|      {-4, 5} : 0 <----- 0 : {-1, 3} |
|                     0               |
|                                     |
|      {-4, 6} : 0 <----- 0 : {-1, 4} |
|                     0               |
|                                     |
|      {-1, -1} : 0 <----- 0 : {2, -3}|
|                      0              |
|                                     |
|      {-1, 0} : 0 <----- 0 : {2, -2} |
|                     0               |
|                                     |
|      {-1, 1} : 0 <----- 0 : {2, -1} |
|                     0               |
|                                     |
|      {-1, 2} : 0 <----- 0 : {2, 0}  |
|                     0               |
|                                     |
|                           1         |
|      {-1, 3} : 0 <----- QQ  : {2, 1}|
|                     0               |
|                                     |
|      {-2, 0} : 0 <----- 0 : {1, -2} |
|                     0               |
|                                     |
|      {-2, 1} : 0 <----- 0 : {1, -1} |
|                     0               |
|                                     |
|      {-2, 2} : 0 <----- 0 : {1, 0}  |
|                     0               |
|                                     |
|      {-2, 3} : 0 <----- 0 : {1, 1}  |
|                     0               |
|                                     |
|      {-2, 4} : 0 <----- 0 : {1, 2}  |
|                     0               |
|                                     |
|      {-3, 1} : 0 <----- 0 : {0, -1} |
|                     0               |
|                                     |
|                           1         |
|      {-3, 2} : 0 <----- QQ  : {0, 0}|
|                     0               |
|                                     |
|      {-3, 3} : 0 <----- 0 : {0, 1}  |
|                     0               |
|                                     |
|      {-3, 4} : 0 <----- 0 : {0, 2}  |
|                     0               |
|                                     |
|      {-3, 5} : 0 <----- 0 : {0, 3}  |
|                     0               |
|                                     |
|      {-4, 2} : 0 <----- 0 : {-1, 0} |
|                     0               |
|                                     |
|o29 : SpectralSequencePageMap        |
+-------------------------------------+

Thus the E^3 page appears to have been computed correctly.

-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2009:0.

connectingMorphism -- use spectral sequences to compute connecting morphisms
****************************************************************************

  * Usage:
        g = connectingMorphism(f, n)
  * Inputs:
      * f, a chain complex map (OldChainComplexes),
      * n, an integer (Macaulay2Doc),
  * Outputs:
      * g, a matrix (Macaulay2Doc),

Description
===========

Given a morphism $f: A \rightarrow B$ of chain complexes returns the connecting
map $H_{n+1}(coker f) \rightarrow H_n (im f)$.

Ways to use connectingMorphism:
===============================

  * connectingMorphism(ChainComplexMap,ZZ)
    -- use spectral sequences to
    compute connecting morphisms

For the programmer
==================

The object connectingMorphism, is a method function (Macaulay2Doc).

-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:3731:0.

connectingMorphism(ChainComplexMap,ZZ) -- use spectral sequences to compute connecting morphisms
************************************************************************************************

  * Function: connectingMorphism,
  * Usage:
        g = connectingMorphism(f, n)
  * Inputs:
      * f, a chain complex map (OldChainComplexes),
      * n, an integer (Macaulay2Doc),
  * Outputs:
      * g, a matrix (Macaulay2Doc),

Description
===========

Given a morphism $f: A \rightarrow B$ of chain complexes returns the connecting
map $H_{n+1}(coker f) \rightarrow H_n (im f)$.

Ways to use this method:
========================

  * connectingMorphism(ChainComplexMap,ZZ)
    -- use spectral sequences to
    compute connecting morphisms
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:3749:0.

degree(Page)
************

  * Function: degree (Macaulay2Doc),

Ways to use this method:
========================

  * degree(Page)
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2348:0.

describe(Page) -- real description
**********************************

  * Function: describe (Macaulay2Doc),
  * Usage:
        describe S
  * Inputs:
      * a Page,

Description
===========

see describe

See also
========

  * describe (Macaulay2Doc) -- real description

Ways to use this method:
========================

  * describe(Page) -- real description
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2483:0.

describe(PageMap) -- real description
*************************************

  * Function: describe (Macaulay2Doc),
  * Usage:
        describe S
  * Inputs:
      * a page map,

Description
===========

see describe

See also
========

  * describe (Macaulay2Doc) -- real description

Ways to use this method:
========================

  * describe(PageMap) -- real description
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2570:0.

describe(SpectralSequence) -- real description
**********************************************

  * Function: describe (Macaulay2Doc),
  * Usage:
        describe S
  * Inputs:
      * a spectral sequence,

Description
===========

see describe

See also
========

  * describe (Macaulay2Doc) -- real description

Ways to use this method:
========================

  * describe(SpectralSequence) -- real
    description
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2195:0.

describe(SpectralSequencePage) -- real description
**************************************************

  * Function: describe (Macaulay2Doc),
  * Usage:
        describe S
  * Inputs:
      * a spectral sequence page,

Description
===========

see describe

See also
========

  * describe (Macaulay2Doc) -- real description

Ways to use this method:
========================

  * describe(SpectralSequencePage),
    -- real description
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2390:0.

describe(SpectralSequencePageMap) -- real description
*****************************************************

  * Function: describe (Macaulay2Doc),
  * Usage:
        describe S
  * Inputs:
      * a spectral sequence page map,

Description
===========

see describe

See also
========

  * describe (Macaulay2Doc) -- real description

Ways to use this method:
========================

  * describe(SpectralSequencePageMap)
    -- real description
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2438:0.

Edge homomorphisms
******************

Suppose that $E$ is a spectral sequence with the properties that:

1. $E^2_{p,q} = 0$ for all $p < l$ and all $q \in \mathbb{Z}$;

2. $E^2_{p,q} = 0 $ for all $q < m$ and all $p \in \mathbb{Z}$;

3.  $E$ converges to the graded module $\{H_n\}$ for $n \in \mathbb{Z}$.

Then $E$ determines a $5$-term exact sequence $H_{l+m+2} \rightarrow
E^2_{l+2,m} \rightarrow E^2_{l,m+1} \rightarrow H_{l+m+1} \rightarrow
E^2_{l+1,m} \rightarrow 0$ which we refer to as the edge complex.

Note that the above properties are satisfied if $E$ is the spectral sequence
determined by a bounded filtration of a bounded chain complex.

The following is an easy example, of a spectral sequence which arises from a
nested chain of simplicial complexes, which illustrates this concept.

+-------------------------------------------------------------------+
|i1 : A = QQ[a,b,c,d];                                              |
+-------------------------------------------------------------------+
|i2 : D = simplicialComplex {a*d*c, a*b, a*c, b*c};                 |
+-------------------------------------------------------------------+
|i3 : F2D = D;                                                      |
+-------------------------------------------------------------------+
|i4 : F1D = simplicialComplex {a*c, d};                             |
+-------------------------------------------------------------------+
|i5 : F0D = simplicialComplex {a,d};                                |
+-------------------------------------------------------------------+
|i6 : K = filteredComplex({F2D, F1D, F0D},ReducedHomology => false);|
+-------------------------------------------------------------------+
|i7 : C = K_infinity;                                               |
+-------------------------------------------------------------------+
|i8 : prune HH C                                                    |
|                                                                   |
|o8 = -1 : 0                                                        |
|                                                                   |
|            1                                                      |
|      0 : QQ                                                       |
|                                                                   |
|            1                                                      |
|      1 : QQ                                                       |
|                                                                   |
|      2 : 0                                                        |
|                                                                   |
|o8 : GradedModule                                                  |
+-------------------------------------------------------------------+

The second page of the corresponding spectral sequences take the form:

+-----------------------------------------------------------------------------+
|i9 : E = spectralSequence(K);                                                |
+-----------------------------------------------------------------------------+
|i10 : e = prune E;                                                           |
+-----------------------------------------------------------------------------+
|i11 : E^2                                                                    |
|                                                                             |
|      +------------------------------------------------+---------------------|
|o11 = |subquotient (| 1 0 1  0 0 0 0 |, | 1  0 0 0 0 |)|subquotient (| 0  |, |
|      |             | 0 0 0  0 0 0 0 |  | 0  0 0 0 0 | |             | -1 |  |
|      |             | 0 0 -1 0 0 0 0 |  | -1 0 0 0 0 | |             | 1  |  |
|      |             | 0 1 0  0 0 0 0 |  | 0  0 0 0 0 | |             | 0  |  |
|      |                                                |             | -1 |  |
|      |{0, 0}                                          |                     |
|      |                                                |{1, 0}               |
|      +------------------------------------------------+---------------------|
|      |image 0                                         |subquotient (| 1 0 0 |
|      |                                                |             | 0 0 0 |
|      |{0, -1}                                         |             | 0 1 0 |
|      |                                                |             | 0 0 1 |
|      |                                                |                     |
|      |                                                |{1, -1}              |
|      |                                                |                     |
|      +------------------------------------------------+---------------------|
|                                                                             |
|o11 : SpectralSequencePage                                                   |
|-----------------------------------------------------------------------------|
|---------------------------------------------+-------------------------------|
|| 0  |)                                      |image 0                        |
|| -1 |                                       |                               |
|| 1  |                                       |{2, 0}                         |
|| 0  |                                       |                               |
|| -1 |                                       |                               |
|                                             |                               |
|                                             |                               |
|---------------------------------------------+-------------------------------|
|1  1  1  0  0  1 0 |, | 1  1  1  0  0  1 0 |)|subquotient (| 0 1  0 0  0 |, ||
|-1 0  0  1  0  0 0 |  | -1 0  0  1  0  0 0 | |             | 0 -1 1 -1 1 |  ||
|0  -1 0  -1 1  0 0 |  | 0  -1 0  -1 1  0 0 | |             | 1 0  0 1  0 |  ||
|0  0  -1 0  -1 0 1 |  | 0  0  -1 0  -1 0 1 | |             | 0 1  0 0  0 |  ||
|                                             |             | 0 0  1 -1 0 |  ||
|                                             |                               |
|                                             |{2, -1}                        |
|---------------------------------------------+-------------------------------|
|-----------------------------------------------------------------------------|
|--------+                                                                    |
|        |                                                                    |
|        |                                                                    |
|        |                                                                    |
|        |                                                                    |
|        |                                                                    |
|        |                                                                    |
|        |                                                                    |
|--------+                                                                    |
| 0  0 |)|                                                                    |
| -1 1 | |                                                                    |
| 1  0 | |                                                                    |
| 0  0 | |                                                                    |
| -1 0 | |                                                                    |
|        |                                                                    |
|        |                                                                    |
|--------+                                                                    |
+-----------------------------------------------------------------------------+
|i12 : e^2                                                                    |
|                                                                             |
|      +-------+-------+-------+                                              |
|      |  2    |       |       |                                              |
|o12 = |QQ     |0      |0      |                                              |
|      |       |       |       |                                              |
|      |{0, 0} |{1, 0} |{2, 0} |                                              |
|      +-------+-------+-------+                                              |
|      |       |       |  2    |                                              |
|      |0      |0      |QQ     |                                              |
|      |       |       |       |                                              |
|      |{0, -1}|{1, -1}|{2, -1}|                                              |
|      +-------+-------+-------+                                              |
|                                                                             |
|o12 : SpectralSequencePage                                                   |
+-----------------------------------------------------------------------------+

The acyclic edge complex for this example has the form $H_1(C) \rightarrow
E^2_{2,-1} \rightarrow E^2_{0,0} \rightarrow H_0(C)  \rightarrow E^2_{1, -1}
\rightarrow 0$ and is given by

+-----------------------------------------------------------------------------+
|i13 : edgeComplex E                                                          |
|                                                                             |
|o13 = subquotient (| 1 0 0 1  1  1  0  0  1 0 |, | 1  1  1  0  0  1 0 |) <-- |
|                   | 0 0 0 -1 0  0  1  0  0 0 |  | -1 0  0  1  0  0 0 |      |
|                   | 0 1 0 0  -1 0  -1 1  0 0 |  | 0  -1 0  -1 1  0 0 |      |
|                   | 0 0 1 0  0  -1 0  -1 0 1 |  | 0  0  -1 0  -1 0 1 |      |
|                                                                             |
|      0                                                                      |
|                                                                             |
|                                                                             |
|o13 : ChainComplex                                                           |
|-----------------------------------------------------------------------------|
|cokernel | 1  1  1  0  0  | <-- subquotient (| 1 0 1  0 0 0 0 |, | 1  0 0 0 0|
|         | -1 0  0  1  0  |                  | 0 0 0  0 0 0 0 |  | 0  0 0 0 0|
|         | 0  -1 0  -1 1  |                  | 0 0 -1 0 0 0 0 |  | -1 0 0 0 0|
|         | 0  0  -1 0  -1 |                  | 0 1 0  0 0 0 0 |  | 0  0 0 0 0|
|                                                                             |
|1                               2                                            |
|                                                                             |
|-----------------------------------------------------------------------------|
||) <-- subquotient (| 0 1  0 0  0 |, | 0  0 |) <-- subquotient (| 1  0  |, | |
||                   | 0 -1 1 -1 1 |  | -1 1 |                   | -1 1  |  | |
||                   | 1 0  0 1  0 |  | 1  0 |                   | 0  -1 |  | |
||                   | 0 1  0 0  0 |  | 0  0 |                   | 1  0  |  | |
|                    | 0 0  1 -1 0 |  | -1 0 |                   | 0  1  |  | |
|                                                                             |
|       3                                           4                         |
|-----------------------------------------------------------------------------|
|0  |)                                                                        |
|-1 |                                                                         |
|1  |                                                                         |
|0  |                                                                         |
|-1 |                                                                         |
+-----------------------------------------------------------------------------+
|i14 : prune edgeComplex E                                                    |
|                                                                             |
|              1       2       2       1                                      |
|o14 = 0 <-- QQ  <-- QQ  <-- QQ  <-- QQ                                       |
|                                                                             |
|      0     1       2       3       4                                        |
|                                                                             |
|o14 : ChainComplex                                                           |
+-----------------------------------------------------------------------------+

To see that it is acyclic we can compute

+----------------------------+
|i15 : prune HH edgeComplex E|
|                            |
|o15 = 0 : 0                 |
|                            |
|      1 : 0                 |
|                            |
|      2 : 0                 |
|                            |
|      3 : 0                 |
|                            |
|      4 : 0                 |
|                            |
|o15 : GradedModule          |
+----------------------------+

Caveat
======

The method currently does not support pruned spectral sequences.

See also
========

  * Examples of filtered complexes and spectral sequences
    -- How to use this package
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:3961:0.

edgeComplex -- the edge homomorphisms
*************************************

  * Usage:
        C = edgeComplex E
  * Inputs:
      * E, a spectral sequence,
  * Outputs:
      * C, a chain complex (OldChainComplexes),

Description
===========

Suppose that $E$ is a spectral sequence with the properties that:

1. $E^2_{p,q} = 0$ for all $p < l$ and all $q \in \mathbb{Z}$;

2. $E^2_{p,q} = 0 $ for all $q < m$ and all $p \in \mathbb{Z}$;

3.  $E$ converges to the graded module $\{H_n\}$ for $n \in \mathbb{Z}$.

Then $E$ determines a $5$-term exact sequence $H_{l+m+2} \rightarrow
E^2_{l+2,m} \rightarrow E^2_{l,m+1} \rightarrow H_{l+m+1} \rightarrow
E^2_{l+1,m} \rightarrow 0$ which we refer to as the edge complex.

Note that the above properties are satisfied if $E$ is the spectral sequence
determined by a bounded filtration of a bounded chain complex.

The following is an easy example, of a spectral sequence which arises from a
nested chain of simplicial complexes, which illustrates this concept.

+-------------------------------------------------------------------+
|i1 : A = QQ[a,b,c,d];                                              |
+-------------------------------------------------------------------+
|i2 : D = simplicialComplex {a*d*c, a*b, a*c, b*c};                 |
+-------------------------------------------------------------------+
|i3 : F2D = D;                                                      |
+-------------------------------------------------------------------+
|i4 : F1D = simplicialComplex {a*c, d};                             |
+-------------------------------------------------------------------+
|i5 : F0D = simplicialComplex {a,d};                                |
+-------------------------------------------------------------------+
|i6 : K = filteredComplex({F2D, F1D, F0D},ReducedHomology => false);|
+-------------------------------------------------------------------+
|i7 : C = K_infinity;                                               |
+-------------------------------------------------------------------+
|i8 : prune HH C                                                    |
|                                                                   |
|o8 = -1 : 0                                                        |
|                                                                   |
|            1                                                      |
|      0 : QQ                                                       |
|                                                                   |
|            1                                                      |
|      1 : QQ                                                       |
|                                                                   |
|      2 : 0                                                        |
|                                                                   |
|o8 : GradedModule                                                  |
+-------------------------------------------------------------------+

The second page of the corresponding spectral sequences take the form:

+-----------------------------------------------------------------------------+
|i9 : E = spectralSequence(K);                                                |
+-----------------------------------------------------------------------------+
|i10 : e = prune E;                                                           |
+-----------------------------------------------------------------------------+
|i11 : E^2                                                                    |
|                                                                             |
|      +------------------------------------------------+---------------------|
|o11 = |subquotient (| 1 0 1  0 0 0 0 |, | 1  0 0 0 0 |)|subquotient (| 0  |, |
|      |             | 0 0 0  0 0 0 0 |  | 0  0 0 0 0 | |             | -1 |  |
|      |             | 0 0 -1 0 0 0 0 |  | -1 0 0 0 0 | |             | 1  |  |
|      |             | 0 1 0  0 0 0 0 |  | 0  0 0 0 0 | |             | 0  |  |
|      |                                                |             | -1 |  |
|      |{0, 0}                                          |                     |
|      |                                                |{1, 0}               |
|      +------------------------------------------------+---------------------|
|      |image 0                                         |subquotient (| 1 0 0 |
|      |                                                |             | 0 0 0 |
|      |{0, -1}                                         |             | 0 1 0 |
|      |                                                |             | 0 0 1 |
|      |                                                |                     |
|      |                                                |{1, -1}              |
|      |                                                |                     |
|      +------------------------------------------------+---------------------|
|                                                                             |
|o11 : SpectralSequencePage                                                   |
|-----------------------------------------------------------------------------|
|---------------------------------------------+-------------------------------|
|| 0  |)                                      |image 0                        |
|| -1 |                                       |                               |
|| 1  |                                       |{2, 0}                         |
|| 0  |                                       |                               |
|| -1 |                                       |                               |
|                                             |                               |
|                                             |                               |
|---------------------------------------------+-------------------------------|
|1  1  1  0  0  1 0 |, | 1  1  1  0  0  1 0 |)|subquotient (| 0 1  0 0  0 |, ||
|-1 0  0  1  0  0 0 |  | -1 0  0  1  0  0 0 | |             | 0 -1 1 -1 1 |  ||
|0  -1 0  -1 1  0 0 |  | 0  -1 0  -1 1  0 0 | |             | 1 0  0 1  0 |  ||
|0  0  -1 0  -1 0 1 |  | 0  0  -1 0  -1 0 1 | |             | 0 1  0 0  0 |  ||
|                                             |             | 0 0  1 -1 0 |  ||
|                                             |                               |
|                                             |{2, -1}                        |
|---------------------------------------------+-------------------------------|
|-----------------------------------------------------------------------------|
|--------+                                                                    |
|        |                                                                    |
|        |                                                                    |
|        |                                                                    |
|        |                                                                    |
|        |                                                                    |
|        |                                                                    |
|        |                                                                    |
|--------+                                                                    |
| 0  0 |)|                                                                    |
| -1 1 | |                                                                    |
| 1  0 | |                                                                    |
| 0  0 | |                                                                    |
| -1 0 | |                                                                    |
|        |                                                                    |
|        |                                                                    |
|--------+                                                                    |
+-----------------------------------------------------------------------------+
|i12 : e^2                                                                    |
|                                                                             |
|      +-------+-------+-------+                                              |
|      |  2    |       |       |                                              |
|o12 = |QQ     |0      |0      |                                              |
|      |       |       |       |                                              |
|      |{0, 0} |{1, 0} |{2, 0} |                                              |
|      +-------+-------+-------+                                              |
|      |       |       |  2    |                                              |
|      |0      |0      |QQ     |                                              |
|      |       |       |       |                                              |
|      |{0, -1}|{1, -1}|{2, -1}|                                              |
|      +-------+-------+-------+                                              |
|                                                                             |
|o12 : SpectralSequencePage                                                   |
+-----------------------------------------------------------------------------+

The acyclic edge complex for this example has the form $H_1(C) \rightarrow
E^2_{2,-1} \rightarrow E^2_{0,0} \rightarrow H_0(C)  \rightarrow E^2_{1, -1}
\rightarrow 0$ and is given by

+-----------------------------------------------------------------------------+
|i13 : edgeComplex E                                                          |
|                                                                             |
|o13 = subquotient (| 1 0 0 1  1  1  0  0  1 0 |, | 1  1  1  0  0  1 0 |) <-- |
|                   | 0 0 0 -1 0  0  1  0  0 0 |  | -1 0  0  1  0  0 0 |      |
|                   | 0 1 0 0  -1 0  -1 1  0 0 |  | 0  -1 0  -1 1  0 0 |      |
|                   | 0 0 1 0  0  -1 0  -1 0 1 |  | 0  0  -1 0  -1 0 1 |      |
|                                                                             |
|      0                                                                      |
|                                                                             |
|                                                                             |
|o13 : ChainComplex                                                           |
|-----------------------------------------------------------------------------|
|cokernel | 1  1  1  0  0  | <-- subquotient (| 1 0 1  0 0 0 0 |, | 1  0 0 0 0|
|         | -1 0  0  1  0  |                  | 0 0 0  0 0 0 0 |  | 0  0 0 0 0|
|         | 0  -1 0  -1 1  |                  | 0 0 -1 0 0 0 0 |  | -1 0 0 0 0|
|         | 0  0  -1 0  -1 |                  | 0 1 0  0 0 0 0 |  | 0  0 0 0 0|
|                                                                             |
|1                               2                                            |
|                                                                             |
|-----------------------------------------------------------------------------|
||) <-- subquotient (| 0 1  0 0  0 |, | 0  0 |) <-- subquotient (| 1  0  |, | |
||                   | 0 -1 1 -1 1 |  | -1 1 |                   | -1 1  |  | |
||                   | 1 0  0 1  0 |  | 1  0 |                   | 0  -1 |  | |
||                   | 0 1  0 0  0 |  | 0  0 |                   | 1  0  |  | |
|                    | 0 0  1 -1 0 |  | -1 0 |                   | 0  1  |  | |
|                                                                             |
|       3                                           4                         |
|-----------------------------------------------------------------------------|
|0  |)                                                                        |
|-1 |                                                                         |
|1  |                                                                         |
|0  |                                                                         |
|-1 |                                                                         |
+-----------------------------------------------------------------------------+
|i14 : prune edgeComplex E                                                    |
|                                                                             |
|              1       2       2       1                                      |
|o14 = 0 <-- QQ  <-- QQ  <-- QQ  <-- QQ                                       |
|                                                                             |
|      0     1       2       3       4                                        |
|                                                                             |
|o14 : ChainComplex                                                           |
+-----------------------------------------------------------------------------+

To see that it is acyclic we can compute

+----------------------------+
|i15 : prune HH edgeComplex E|
|                            |
|o15 = 0 : 0                 |
|                            |
|      1 : 0                 |
|                            |
|      2 : 0                 |
|                            |
|      3 : 0                 |
|                            |
|      4 : 0                 |
|                            |
|o15 : GradedModule          |
+----------------------------+

Caveat
======

The method currently does not support pruned spectral sequences.

Ways to use edgeComplex:
========================

  * "edgeComplex(SpectralSequence)"

For the programmer
==================

The object edgeComplex, is a method function (Macaulay2Doc).

-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:4023:0.

Example 1 -- Easy example of a filtered simplicial complex
**********************************************************

Here we provide an easy example of a filtered simplicial complex and the
resulting spectral sequence.  This example is small enough that all aspects of
it can be explicitly computed by hand.

+-----------------------------------------------------------------+
|i1 : A = QQ[a,b,c,d];                                            |
+-----------------------------------------------------------------+
|i2 : D = simplicialComplex {a*d*c, a*b, a*c, b*c};               |
+-----------------------------------------------------------------+
|i3 : F2D = D                                                     |
|                                                                 |
|o3 = simplicialComplex | bc ab acd |                             |
|                                                                 |
|o3 : SimplicialComplex                                           |
+-----------------------------------------------------------------+
|i4 : F1D = simplicialComplex {a*c, d}                            |
|                                                                 |
|o4 = simplicialComplex | d ac |                                  |
|                                                                 |
|o4 : SimplicialComplex                                           |
+-----------------------------------------------------------------+
|i5 : F0D = simplicialComplex {a,d}                               |
|                                                                 |
|o5 = simplicialComplex | d a |                                   |
|                                                                 |
|o5 : SimplicialComplex                                           |
+-----------------------------------------------------------------+
|i6 : K= filteredComplex({F2D, F1D, F0D},ReducedHomology => false)|
|                                                                 |
|o6 = -1 : image 0 <-- image 0 <-- image 0 <-- image 0            |
|                                                                 |
|          -1          0           1           2                  |
|                                                                 |
|     0 : image 0 <-- image | 1 0 | <-- image 0 <-- image 0       |
|                           | 0 0 |                               |
|         -1                | 0 0 |     1           2             |
|                           | 0 1 |                               |
|                                                                 |
|                     0                                           |
|                                                                 |
|     1 : image 0 <-- image | 1 0 0 | <-- image | 0 | <-- image 0 |
|                           | 0 0 0 |           | 1 |             |
|         -1                | 0 1 0 |           | 0 |     2       |
|                           | 0 0 1 |           | 0 |             |
|                                               | 0 |             |
|                     0                                           |
|                                         1                       |
|                                                                 |
|                       4       5       1                         |
|     2 : image 0 <-- QQ  <-- QQ  <-- QQ                          |
|                                                                 |
|         -1          0       1       2                           |
|                                                                 |
|o6 : FilteredComplex                                             |
+-----------------------------------------------------------------+
|i7 : E = prune spectralSequence(K)                               |
|                                                                 |
|o7 = E                                                           |
|                                                                 |
|o7 : SpectralSequence                                            |
+-----------------------------------------------------------------+
|i8 : E^0                                                         |
|                                                                 |
|     +-------+-------+-------+                                   |
|     |  2    |  1    |  1    |                                   |
|o8 = |QQ     |QQ     |QQ     |                                   |
|     |       |       |       |                                   |
|     |{0, 0} |{1, 0} |{2, 0} |                                   |
|     +-------+-------+-------+                                   |
|     |       |  1    |  4    |                                   |
|     |0      |QQ     |QQ     |                                   |
|     |       |       |       |                                   |
|     |{0, -1}|{1, -1}|{2, -1}|                                   |
|     +-------+-------+-------+                                   |
|     |       |       |  1    |                                   |
|     |0      |0      |QQ     |                                   |
|     |       |       |       |                                   |
|     |{0, -2}|{1, -2}|{2, -2}|                                   |
|     +-------+-------+-------+                                   |
|                                                                 |
|o8 : SpectralSequencePage                                        |
+-----------------------------------------------------------------+
|i9 : E^1                                                         |
|                                                                 |
|     +-------+-------+-------+                                   |
|     |  2    |       |       |                                   |
|o9 = |QQ     |0      |0      |                                   |
|     |       |       |       |                                   |
|     |{0, 0} |{1, 0} |{2, 0} |                                   |
|     +-------+-------+-------+                                   |
|     |       |       |  2    |                                   |
|     |0      |0      |QQ     |                                   |
|     |       |       |       |                                   |
|     |{0, -1}|{1, -1}|{2, -1}|                                   |
|     +-------+-------+-------+                                   |
|                                                                 |
|o9 : SpectralSequencePage                                        |
+-----------------------------------------------------------------+
|i10 : E^2                                                        |
|                                                                 |
|      +-------+-------+-------+                                  |
|      |  2    |       |       |                                  |
|o10 = |QQ     |0      |0      |                                  |
|      |       |       |       |                                  |
|      |{0, 0} |{1, 0} |{2, 0} |                                  |
|      +-------+-------+-------+                                  |
|      |       |       |  2    |                                  |
|      |0      |0      |QQ     |                                  |
|      |       |       |       |                                  |
|      |{0, -1}|{1, -1}|{2, -1}|                                  |
|      +-------+-------+-------+                                  |
|                                                                 |
|o10 : SpectralSequencePage                                       |
+-----------------------------------------------------------------+
|i11 : E^3                                                        |
|                                                                 |
|      +-------+-------+-------+                                  |
|      |  1    |       |       |                                  |
|o11 = |QQ     |0      |0      |                                  |
|      |       |       |       |                                  |
|      |{0, 0} |{1, 0} |{2, 0} |                                  |
|      +-------+-------+-------+                                  |
|      |       |       |  1    |                                  |
|      |0      |0      |QQ     |                                  |
|      |       |       |       |                                  |
|      |{0, -1}|{1, -1}|{2, -1}|                                  |
|      +-------+-------+-------+                                  |
|                                                                 |
|o11 : SpectralSequencePage                                       |
+-----------------------------------------------------------------+
|i12 : E^infinity                                                 |
|                                                                 |
|      +-------+-------+-------+                                  |
|      |  1    |       |       |                                  |
|o12 = |QQ     |0      |0      |                                  |
|      |       |       |       |                                  |
|      |{0, 0} |{1, 0} |{2, 0} |                                  |
|      +-------+-------+-------+                                  |
|      |       |       |  1    |                                  |
|      |0      |0      |QQ     |                                  |
|      |       |       |       |                                  |
|      |{0, -1}|{1, -1}|{2, -1}|                                  |
|      +-------+-------+-------+                                  |
|                                                                 |
|o12 : Page                                                       |
+-----------------------------------------------------------------+
|i13 : C = K_infinity                                             |
|                                                                 |
|                    4       5       1                            |
|o13 = image 0 <-- QQ  <-- QQ  <-- QQ                             |
|                                                                 |
|      -1          0       1       2                              |
|                                                                 |
|o13 : ChainComplex                                               |
+-----------------------------------------------------------------+
|i14 : prune HH C                                                 |
|                                                                 |
|o14 = -1 : 0                                                     |
|                                                                 |
|             1                                                   |
|       0 : QQ                                                    |
|                                                                 |
|             1                                                   |
|       1 : QQ                                                    |
|                                                                 |
|       2 : 0                                                     |
|                                                                 |
|o14 : GradedModule                                               |
+-----------------------------------------------------------------+
|i15 : E^2 .dd                                                    |
|                                                                 |
|o15 = {-3, 2} : 0 <----- 0 : {-1, 1}                             |
|                     0                                           |
|                                                                 |
|      {-3, 3} : 0 <----- 0 : {-1, 2}                             |
|                     0                                           |
|                                                                 |
|      {-3, 4} : 0 <----- 0 : {-1, 3}                             |
|                     0                                           |
|                                                                 |
|      {0, -2} : 0 <----- 0 : {2, -3}                             |
|                     0                                           |
|                                                                 |
|      {0, -1} : 0 <----- 0 : {2, -2}                             |
|                     0                                           |
|                                                                 |
|                 2                 2                             |
|      {0, 0} : QQ  <------------ QQ  : {2, -1}                   |
|                      | 0 1  |                                   |
|                      | 0 -1 |                                   |
|                                                                 |
|      {0, 1} : 0 <----- 0 : {2, 0}                               |
|                    0                                            |
|                                                                 |
|      {-1, -1} : 0 <----- 0 : {1, -2}                            |
|                      0                                          |
|                                                                 |
|      {-1, 0} : 0 <----- 0 : {1, -1}                             |
|                     0                                           |
|                                                                 |
|      {-1, 1} : 0 <----- 0 : {1, 0}                              |
|                     0                                           |
|                                                                 |
|      {-1, 2} : 0 <----- 0 : {1, 1}                              |
|                     0                                           |
|                                                                 |
|      {-2, 0} : 0 <----- 0 : {0, -1}                             |
|                     0                                           |
|                                                                 |
|                           2                                     |
|      {-2, 1} : 0 <----- QQ  : {0, 0}                            |
|                     0                                           |
|                                                                 |
|      {-2, 2} : 0 <----- 0 : {0, 1}                              |
|                     0                                           |
|                                                                 |
|      {-2, 3} : 0 <----- 0 : {0, 2}                              |
|                     0                                           |
|                                                                 |
|      {-3, 1} : 0 <----- 0 : {-1, 0}                             |
|                     0                                           |
|                                                                 |
|o15 : SpectralSequencePageMap                                    |
+-----------------------------------------------------------------+

Considering the $E^2$ and $E^3$ pages of the spectral sequence we conclude that
the map $d^2_{2,-1}$ must have a $1$-dimensional image and a $1$-dimensional
kernel.  This can be verified easily:

+-------------------------------+
|i16 : rank ker E^2 .dd_{2,-1}  |
|                               |
|o16 = 1                        |
+-------------------------------+
|i17 : rank image E^2 .dd_{2,-1}|
|                               |
|o17 = 1                        |
+-------------------------------+
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:4096:0.

Example 2 -- Easy example of a filtered simplicial complex
**********************************************************

We provide an easy example of a filtered simplicial complex and the resulting
spectral sequence.  This example is small enough that all aspects of it can be
explicitly computed by hand.

+---------------------------------------------------------------------+
|i1 : A = QQ[a,b,c];                                                  |
+---------------------------------------------------------------------+
|i2 : D = simplicialComplex({a*b*c})                                  |
|                                                                     |
|o2 = simplicialComplex | abc |                                       |
|                                                                     |
|o2 : SimplicialComplex                                               |
+---------------------------------------------------------------------+
|i3 : F3D = D;                                                        |
+---------------------------------------------------------------------+
|i4 : F2D = simplicialComplex({a*b,a*c,b*c})                          |
|                                                                     |
|o4 = simplicialComplex | bc ac ab |                                  |
|                                                                     |
|o4 : SimplicialComplex                                               |
+---------------------------------------------------------------------+
|i5 : F1D = simplicialComplex({a*b,c})                                |
|                                                                     |
|o5 = simplicialComplex | c ab |                                      |
|                                                                     |
|o5 : SimplicialComplex                                               |
+---------------------------------------------------------------------+
|i6 : F0D = simplicialComplex({a,b})                                  |
|                                                                     |
|o6 = simplicialComplex | b a |                                       |
|                                                                     |
|o6 : SimplicialComplex                                               |
+---------------------------------------------------------------------+
|i7 : K = filteredComplex({F3D,F2D,F1D,F0D}, ReducedHomology => false)|
|                                                                     |
|o7 = -1 : image 0 <-- image 0 <-- image 0 <-- image 0                |
|                                                                     |
|          -1          0           1           2                      |
|                                                                     |
|     0 : image 0 <-- image | 1 0 | <-- image 0 <-- image 0           |
|                           | 0 1 |                                   |
|         -1                | 0 0 |     1           2                 |
|                                                                     |
|                     0                                               |
|                                                                     |
|     1 : image 0 <-- image | 1 0 0 | <-- image | 1 | <-- image 0     |
|                           | 0 1 0 |           | 0 |                 |
|         -1                | 0 0 1 |           | 0 |     2           |
|                                                                     |
|                     0                   1                           |
|                                                                     |
|     2 : image 0 <-- image | 1 0 0 | <-- image | 1 0 0 | <-- image 0 |
|                           | 0 1 0 |           | 0 1 0 |             |
|         -1                | 0 0 1 |           | 0 0 1 |     2       |
|                                                                     |
|                     0                   1                           |
|                                                                     |
|                       3       3       1                             |
|     3 : image 0 <-- QQ  <-- QQ  <-- QQ                              |
|                                                                     |
|         -1          0       1       2                               |
|                                                                     |
|o7 : FilteredComplex                                                 |
+---------------------------------------------------------------------+
|i8 : E = prune spectralSequence K                                    |
|                                                                     |
|o8 = E                                                               |
|                                                                     |
|o8 : SpectralSequence                                                |
+---------------------------------------------------------------------+
|i9 : E^0                                                             |
|                                                                     |
|     +-------+-------+-------+-------+                               |
|     |  2    |  1    |       |       |                               |
|o9 = |QQ     |QQ     |0      |0      |                               |
|     |       |       |       |       |                               |
|     |{0, 0} |{1, 0} |{2, 0} |{3, 0} |                               |
|     +-------+-------+-------+-------+                               |
|     |       |  1    |  2    |  1    |                               |
|     |0      |QQ     |QQ     |QQ     |                               |
|     |       |       |       |       |                               |
|     |{0, -1}|{1, -1}|{2, -1}|{3, -1}|                               |
|     +-------+-------+-------+-------+                               |
|                                                                     |
|o9 : SpectralSequencePage                                            |
+---------------------------------------------------------------------+
|i10 : E^0 .dd                                                        |
|                                                                     |
|o10 = {3, -4} : 0 <----- 0 : {3, -3}                                 |
|                     0                                               |
|                                                                     |
|      {-1, 0} : 0 <----- 0 : {-1, 1}                                 |
|                     0                                               |
|                                                                     |
|      {3, -3} : 0 <----- 0 : {3, -2}                                 |
|                     0                                               |
|                                                                     |
|      {-1, 1} : 0 <----- 0 : {-1, 2}                                 |
|                     0                                               |
|                                                                     |
|                           1                                         |
|      {3, -2} : 0 <----- QQ  : {3, -1}                               |
|                     0                                               |
|                                                                     |
|      {-1, 2} : 0 <----- 0 : {-1, 3}                                 |
|                     0                                               |
|                                                                     |
|      {2, -4} : 0 <----- 0 : {2, -3}                                 |
|                     0                                               |
|                                                                     |
|      {2, -3} : 0 <----- 0 : {2, -2}                                 |
|                     0                                               |
|                                                                     |
|                           2                                         |
|      {2, -2} : 0 <----- QQ  : {2, -1}                               |
|                     0                                               |
|                                                                     |
|                  2                                                  |
|      {2, -1} : QQ  <----- 0 : {2, 0}                                |
|                       0                                             |
|                                                                     |
|      {1, -3} : 0 <----- 0 : {1, -2}                                 |
|                     0                                               |
|                                                                     |
|                           1                                         |
|      {1, -2} : 0 <----- QQ  : {1, -1}                               |
|                     0                                               |
|                                                                     |
|                  1          1                                       |
|      {1, -1} : QQ  <----- QQ  : {1, 0}                              |
|                       0                                             |
|                                                                     |
|                 1                                                   |
|      {1, 0} : QQ  <----- 0 : {1, 1}                                 |
|                      0                                              |
|                                                                     |
|      {0, -2} : 0 <----- 0 : {0, -1}                                 |
|                     0                                               |
|                                                                     |
|                           2                                         |
|      {0, -1} : 0 <----- QQ  : {0, 0}                                |
|                     0                                               |
|                                                                     |
|                 2                                                   |
|      {0, 0} : QQ  <----- 0 : {0, 1}                                 |
|                      0                                              |
|                                                                     |
|      {0, 1} : 0 <----- 0 : {0, 2}                                   |
|                    0                                                |
|                                                                     |
|      {3, -5} : 0 <----- 0 : {3, -4}                                 |
|                     0                                               |
|                                                                     |
|      {-1, -1} : 0 <----- 0 : {-1, 0}                                |
|                      0                                              |
|                                                                     |
|o10 : SpectralSequencePageMap                                        |
+---------------------------------------------------------------------+
|i11 : E^0                                                            |
|                                                                     |
|      +-------+-------+-------+-------+                              |
|      |  2    |  1    |       |       |                              |
|o11 = |QQ     |QQ     |0      |0      |                              |
|      |       |       |       |       |                              |
|      |{0, 0} |{1, 0} |{2, 0} |{3, 0} |                              |
|      +-------+-------+-------+-------+                              |
|      |       |  1    |  2    |  1    |                              |
|      |0      |QQ     |QQ     |QQ     |                              |
|      |       |       |       |       |                              |
|      |{0, -1}|{1, -1}|{2, -1}|{3, -1}|                              |
|      +-------+-------+-------+-------+                              |
|                                                                     |
|o11 : SpectralSequencePage                                           |
+---------------------------------------------------------------------+
|i12 : E^1                                                            |
|                                                                     |
|      +-------+-------+-------+-------+                              |
|      |  2    |  1    |       |       |                              |
|o12 = |QQ     |QQ     |0      |0      |                              |
|      |       |       |       |       |                              |
|      |{0, 0} |{1, 0} |{2, 0} |{3, 0} |                              |
|      +-------+-------+-------+-------+                              |
|      |       |  1    |  2    |  1    |                              |
|      |0      |QQ     |QQ     |QQ     |                              |
|      |       |       |       |       |                              |
|      |{0, -1}|{1, -1}|{2, -1}|{3, -1}|                              |
|      +-------+-------+-------+-------+                              |
|                                                                     |
|o12 : SpectralSequencePage                                           |
+---------------------------------------------------------------------+
|i13 : E^0 .dd_{1,0}                                                  |
|                                                                     |
|o13 = 0                                                              |
|                                                                     |
|               1       1                                             |
|o13 : Matrix QQ  <-- QQ                                              |
+---------------------------------------------------------------------+
|i14 : E^1 .dd                                                        |
|                                                                     |
|o14 = {2, -3} : 0 <----- 0 : {3, -3}                                 |
|                     0                                               |
|                                                                     |
|      {-2, 1} : 0 <----- 0 : {-1, 1}                                 |
|                     0                                               |
|                                                                     |
|      {2, -2} : 0 <----- 0 : {3, -2}                                 |
|                     0                                               |
|                                                                     |
|      {-2, 2} : 0 <----- 0 : {-1, 2}                                 |
|                     0                                               |
|                                                                     |
|                  2               1                                  |
|      {2, -1} : QQ  <---------- QQ  : {3, -1}                        |
|                       | 1  |                                        |
|                       | -1 |                                        |
|                                                                     |
|      {-2, 3} : 0 <----- 0 : {-1, 3}                                 |
|                     0                                               |
|                                                                     |
|      {1, -3} : 0 <----- 0 : {2, -3}                                 |
|                     0                                               |
|                                                                     |
|      {1, -2} : 0 <----- 0 : {2, -2}                                 |
|                     0                                               |
|                                                                     |
|                  1                  2                               |
|      {1, -1} : QQ  <------------- QQ  : {2, -1}                     |
|                       | -1 -1 |                                     |
|                                                                     |
|                 1                                                   |
|      {1, 0} : QQ  <----- 0 : {2, 0}                                 |
|                      0                                              |
|                                                                     |
|      {0, -2} : 0 <----- 0 : {1, -2}                                 |
|                     0                                               |
|                                                                     |
|                           1                                         |
|      {0, -1} : 0 <----- QQ  : {1, -1}                               |
|                     0                                               |
|                                                                     |
|                 2               1                                   |
|      {0, 0} : QQ  <---------- QQ  : {1, 0}                          |
|                      | 1  |                                         |
|                      | -1 |                                         |
|                                                                     |
|      {0, 1} : 0 <----- 0 : {1, 1}                                   |
|                    0                                                |
|                                                                     |
|      {-1, -1} : 0 <----- 0 : {0, -1}                                |
|                      0                                              |
|                                                                     |
|                           2                                         |
|      {-1, 0} : 0 <----- QQ  : {0, 0}                                |
|                     0                                               |
|                                                                     |
|      {-1, 1} : 0 <----- 0 : {0, 1}                                  |
|                     0                                               |
|                                                                     |
|      {-1, 2} : 0 <----- 0 : {0, 2}                                  |
|                     0                                               |
|                                                                     |
|      {2, -4} : 0 <----- 0 : {3, -4}                                 |
|                     0                                               |
|                                                                     |
|      {-2, 0} : 0 <----- 0 : {-1, 0}                                 |
|                     0                                               |
|                                                                     |
|o14 : SpectralSequencePageMap                                        |
+---------------------------------------------------------------------+
|i15 : E^1                                                            |
|                                                                     |
|      +-------+-------+-------+-------+                              |
|      |  2    |  1    |       |       |                              |
|o15 = |QQ     |QQ     |0      |0      |                              |
|      |       |       |       |       |                              |
|      |{0, 0} |{1, 0} |{2, 0} |{3, 0} |                              |
|      +-------+-------+-------+-------+                              |
|      |       |  1    |  2    |  1    |                              |
|      |0      |QQ     |QQ     |QQ     |                              |
|      |       |       |       |       |                              |
|      |{0, -1}|{1, -1}|{2, -1}|{3, -1}|                              |
|      +-------+-------+-------+-------+                              |
|                                                                     |
|o15 : SpectralSequencePage                                           |
+---------------------------------------------------------------------+
|i16 : E^0                                                            |
|                                                                     |
|      +-------+-------+-------+-------+                              |
|      |  2    |  1    |       |       |                              |
|o16 = |QQ     |QQ     |0      |0      |                              |
|      |       |       |       |       |                              |
|      |{0, 0} |{1, 0} |{2, 0} |{3, 0} |                              |
|      +-------+-------+-------+-------+                              |
|      |       |  1    |  2    |  1    |                              |
|      |0      |QQ     |QQ     |QQ     |                              |
|      |       |       |       |       |                              |
|      |{0, -1}|{1, -1}|{2, -1}|{3, -1}|                              |
|      +-------+-------+-------+-------+                              |
|                                                                     |
|o16 : SpectralSequencePage                                           |
+---------------------------------------------------------------------+
|i17 : E^2                                                            |
|                                                                     |
|      +------+                                                       |
|      |  1   |                                                       |
|o17 = |QQ    |                                                       |
|      |      |                                                       |
|      |{0, 0}|                                                       |
|      +------+                                                       |
|                                                                     |
|o17 : SpectralSequencePage                                           |
+---------------------------------------------------------------------+
|i18 : prune HH K_infinity                                            |
|                                                                     |
|o18 = -1 : 0                                                         |
|                                                                     |
|             1                                                       |
|       0 : QQ                                                        |
|                                                                     |
|       1 : 0                                                         |
|                                                                     |
|       2 : 0                                                         |
|                                                                     |
|o18 : GradedModule                                                   |
+---------------------------------------------------------------------+
|i19 : E^infinity                                                     |
|                                                                     |
|      +------+                                                       |
|      |  1   |                                                       |
|o19 = |QQ    |                                                       |
|      |      |                                                       |
|      |{0, 0}|                                                       |
|      +------+                                                       |
|                                                                     |
|o19 : Page                                                           |
+---------------------------------------------------------------------+
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:4129:0.

Example 3 -- Easy example of a filtered simplicial complex
**********************************************************

We provide an easy example of a filtered simplicial complex and the resulting
spectral sequence.  This example is small enough that all aspects of it can be
explicitly computed by hand.

+--------------------------------------------------------------------+
|i1 : A = QQ[a,b,c]                                                  |
|                                                                    |
|o1 = A                                                              |
|                                                                    |
|o1 : PolynomialRing                                                 |
+--------------------------------------------------------------------+
|i2 : D = simplicialComplex {a*b*c}                                  |
|                                                                    |
|o2 = simplicialComplex | abc |                                      |
|                                                                    |
|o2 : SimplicialComplex                                              |
+--------------------------------------------------------------------+
|i3 : F2D = D                                                        |
|                                                                    |
|o3 = simplicialComplex | abc |                                      |
|                                                                    |
|o3 : SimplicialComplex                                              |
+--------------------------------------------------------------------+
|i4 : F1D = simplicialComplex {a*b,a*c,b*c}                          |
|                                                                    |
|o4 = simplicialComplex | bc ac ab |                                 |
|                                                                    |
|o4 : SimplicialComplex                                              |
+--------------------------------------------------------------------+
|i5 : F0D = simplicialComplex {a,b,c}                                |
|                                                                    |
|o5 = simplicialComplex | c b a |                                    |
|                                                                    |
|o5 : SimplicialComplex                                              |
+--------------------------------------------------------------------+
|i6 : K = filteredComplex({F2D,F1D,F0D}, ReducedHomology => false)   |
|                                                                    |
|o6 = -1 : image 0 <-- image 0 <-- image 0 <-- image 0               |
|                                                                    |
|          -1          0           1           2                     |
|                                                                    |
|     0 : image 0 <-- image | 1 0 0 | <-- image 0 <-- image 0        |
|                           | 0 1 0 |                                |
|         -1                | 0 0 1 |     1           2              |
|                                                                    |
|                     0                                              |
|                                                                    |
|     1 : image 0 <-- image | 1 0 0 | <-- image | 1 0 0 | <-- image 0|
|                           | 0 1 0 |           | 0 1 0 |            |
|         -1                | 0 0 1 |           | 0 0 1 |     2      |
|                                                                    |
|                     0                   1                          |
|                                                                    |
|                       3       3       1                            |
|     2 : image 0 <-- QQ  <-- QQ  <-- QQ                             |
|                                                                    |
|         -1          0       1       2                              |
|                                                                    |
|o6 : FilteredComplex                                                |
+--------------------------------------------------------------------+
|i7 : C = K_infinity                                                 |
|                                                                    |
|                   3       3       1                                |
|o7 = image 0 <-- QQ  <-- QQ  <-- QQ                                 |
|                                                                    |
|     -1          0       1       2                                  |
|                                                                    |
|o7 : ChainComplex                                                   |
+--------------------------------------------------------------------+
|i8 : E = prune spectralSequence K                                   |
|                                                                    |
|o8 = E                                                              |
|                                                                    |
|o8 : SpectralSequence                                               |
+--------------------------------------------------------------------+
|i9 : E^0                                                            |
|                                                                    |
|     +------+------+------+                                         |
|     |  3   |  3   |  1   |                                         |
|o9 = |QQ    |QQ    |QQ    |                                         |
|     |      |      |      |                                         |
|     |{0, 0}|{1, 0}|{2, 0}|                                         |
|     +------+------+------+                                         |
|                                                                    |
|o9 : SpectralSequencePage                                           |
+--------------------------------------------------------------------+
|i10 : E^0 .dd                                                       |
|                                                                    |
|o10 = {-1, 0} : 0 <----- 0 : {-1, 1}                                |
|                     0                                              |
|                                                                    |
|      {-1, 1} : 0 <----- 0 : {-1, 2}                                |
|                     0                                              |
|                                                                    |
|      {-1, 2} : 0 <----- 0 : {-1, 3}                                |
|                     0                                              |
|                                                                    |
|      {2, -4} : 0 <----- 0 : {2, -3}                                |
|                     0                                              |
|                                                                    |
|      {2, -3} : 0 <----- 0 : {2, -2}                                |
|                     0                                              |
|                                                                    |
|      {2, -2} : 0 <----- 0 : {2, -1}                                |
|                     0                                              |
|                                                                    |
|                           1                                        |
|      {2, -1} : 0 <----- QQ  : {2, 0}                               |
|                     0                                              |
|                                                                    |
|      {1, -3} : 0 <----- 0 : {1, -2}                                |
|                     0                                              |
|                                                                    |
|      {1, -2} : 0 <----- 0 : {1, -1}                                |
|                     0                                              |
|                                                                    |
|                           3                                        |
|      {1, -1} : 0 <----- QQ  : {1, 0}                               |
|                     0                                              |
|                                                                    |
|                 3                                                  |
|      {1, 0} : QQ  <----- 0 : {1, 1}                                |
|                      0                                             |
|                                                                    |
|      {0, -2} : 0 <----- 0 : {0, -1}                                |
|                     0                                              |
|                                                                    |
|                           3                                        |
|      {0, -1} : 0 <----- QQ  : {0, 0}                               |
|                     0                                              |
|                                                                    |
|                 3                                                  |
|      {0, 0} : QQ  <----- 0 : {0, 1}                                |
|                      0                                             |
|                                                                    |
|      {0, 1} : 0 <----- 0 : {0, 2}                                  |
|                    0                                               |
|                                                                    |
|      {-1, -1} : 0 <----- 0 : {-1, 0}                               |
|                      0                                             |
|                                                                    |
|o10 : SpectralSequencePageMap                                       |
+--------------------------------------------------------------------+
|i11 : E^1                                                           |
|                                                                    |
|      +------+------+------+                                        |
|      |  3   |  3   |  1   |                                        |
|o11 = |QQ    |QQ    |QQ    |                                        |
|      |      |      |      |                                        |
|      |{0, 0}|{1, 0}|{2, 0}|                                        |
|      +------+------+------+                                        |
|                                                                    |
|o11 : SpectralSequencePage                                          |
+--------------------------------------------------------------------+
|i12 : E^1 .dd                                                       |
|                                                                    |
|o12 = {-2, 1} : 0 <----- 0 : {-1, 1}                                |
|                     0                                              |
|                                                                    |
|      {-2, 2} : 0 <----- 0 : {-1, 2}                                |
|                     0                                              |
|                                                                    |
|      {-2, 3} : 0 <----- 0 : {-1, 3}                                |
|                     0                                              |
|                                                                    |
|      {1, -3} : 0 <----- 0 : {2, -3}                                |
|                     0                                              |
|                                                                    |
|      {1, -2} : 0 <----- 0 : {2, -2}                                |
|                     0                                              |
|                                                                    |
|      {1, -1} : 0 <----- 0 : {2, -1}                                |
|                     0                                              |
|                                                                    |
|                 3               1                                  |
|      {1, 0} : QQ  <---------- QQ  : {2, 0}                         |
|                      | -1 |                                        |
|                      | 1  |                                        |
|                      | -1 |                                        |
|                                                                    |
|      {0, -2} : 0 <----- 0 : {1, -2}                                |
|                     0                                              |
|                                                                    |
|      {0, -1} : 0 <----- 0 : {1, -1}                                |
|                     0                                              |
|                                                                    |
|                 3                     3                            |
|      {0, 0} : QQ  <---------------- QQ  : {1, 0}                   |
|                      | 1  1  0  |                                  |
|                      | -1 0  1  |                                  |
|                      | 0  -1 -1 |                                  |
|                                                                    |
|      {0, 1} : 0 <----- 0 : {1, 1}                                  |
|                    0                                               |
|                                                                    |
|      {-1, -1} : 0 <----- 0 : {0, -1}                               |
|                      0                                             |
|                                                                    |
|                           3                                        |
|      {-1, 0} : 0 <----- QQ  : {0, 0}                               |
|                     0                                              |
|                                                                    |
|      {-1, 1} : 0 <----- 0 : {0, 1}                                 |
|                     0                                              |
|                                                                    |
|      {-1, 2} : 0 <----- 0 : {0, 2}                                 |
|                     0                                              |
|                                                                    |
|      {-2, 0} : 0 <----- 0 : {-1, 0}                                |
|                     0                                              |
|                                                                    |
|o12 : SpectralSequencePageMap                                       |
+--------------------------------------------------------------------+
|i13 : E^2                                                           |
|                                                                    |
|      +------+                                                      |
|      |  1   |                                                      |
|o13 = |QQ    |                                                      |
|      |      |                                                      |
|      |{0, 0}|                                                      |
|      +------+                                                      |
|                                                                    |
|o13 : SpectralSequencePage                                          |
+--------------------------------------------------------------------+
|i14 : E^2 .dd                                                       |
|                                                                    |
|o14 = {-3, 2} : 0 <----- 0 : {-1, 1}                                |
|                     0                                              |
|                                                                    |
|      {-3, 3} : 0 <----- 0 : {-1, 2}                                |
|                     0                                              |
|                                                                    |
|      {-3, 4} : 0 <----- 0 : {-1, 3}                                |
|                     0                                              |
|                                                                    |
|      {0, -2} : 0 <----- 0 : {2, -3}                                |
|                     0                                              |
|                                                                    |
|      {0, -1} : 0 <----- 0 : {2, -2}                                |
|                     0                                              |
|                                                                    |
|                 1                                                  |
|      {0, 0} : QQ  <----- 0 : {2, -1}                               |
|                      0                                             |
|                                                                    |
|      {0, 1} : 0 <----- 0 : {2, 0}                                  |
|                    0                                               |
|                                                                    |
|      {-1, -1} : 0 <----- 0 : {1, -2}                               |
|                      0                                             |
|                                                                    |
|      {-1, 0} : 0 <----- 0 : {1, -1}                                |
|                     0                                              |
|                                                                    |
|      {-1, 1} : 0 <----- 0 : {1, 0}                                 |
|                     0                                              |
|                                                                    |
|      {-1, 2} : 0 <----- 0 : {1, 1}                                 |
|                     0                                              |
|                                                                    |
|      {-2, 0} : 0 <----- 0 : {0, -1}                                |
|                     0                                              |
|                                                                    |
|                           1                                        |
|      {-2, 1} : 0 <----- QQ  : {0, 0}                               |
|                     0                                              |
|                                                                    |
|      {-2, 2} : 0 <----- 0 : {0, 1}                                 |
|                     0                                              |
|                                                                    |
|      {-2, 3} : 0 <----- 0 : {0, 2}                                 |
|                     0                                              |
|                                                                    |
|      {-3, 1} : 0 <----- 0 : {-1, 0}                                |
|                     0                                              |
|                                                                    |
|o14 : SpectralSequencePageMap                                       |
+--------------------------------------------------------------------+
|i15 : E^infinity                                                    |
|                                                                    |
|      +------+                                                      |
|      |  1   |                                                      |
|o15 = |QQ    |                                                      |
|      |      |                                                      |
|      |{0, 0}|                                                      |
|      +------+                                                      |
|                                                                    |
|o15 : Page                                                          |
+--------------------------------------------------------------------+
|i16 : prune HH K_infinity                                           |
|                                                                    |
|o16 = -1 : 0                                                        |
|                                                                    |
|             1                                                      |
|       0 : QQ                                                       |
|                                                                    |
|       1 : 0                                                        |
|                                                                    |
|       2 : 0                                                        |
|                                                                    |
|o16 : GradedModule                                                  |
+--------------------------------------------------------------------+
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:4159:0.

Examples of change of rings Spectral Sequences
**********************************************

Here are some examples of change of rings spectral sequences.

Given a ring map f: R -> S, an R-module M and an R-module S, there is a
spectral sequence E with E^2_{p,q} = Tor^S_p(Tor^R_q(M,S),N) that abuts to
Tor^R_{p+q}(M,N).

+-----------------------------------------------------------------------------+
|i1 : k=QQ;                                                                   |
+-----------------------------------------------------------------------------+
|i2 : R=k[a,b,c];                                                             |
+-----------------------------------------------------------------------------+
|i3 : S=k[s,t];                                                               |
+-----------------------------------------------------------------------------+
|i4 : f = map(S,R,{s^2,s*t,t^2});                                             |
|                                                                             |
|o4 : RingMap S <-- R                                                         |
+-----------------------------------------------------------------------------+
|i5 : N = coker vars S;                                                       |
+-----------------------------------------------------------------------------+
|i6 : M = coker vars R --;                                                    |
|                                                                             |
|o6 = cokernel | a b c |                                                      |
|                                                                             |
|                            1                                                |
|o6 : R-module, quotient of R                                                 |
+-----------------------------------------------------------------------------+
|i7 : F := complete res N;                                                    |
+-----------------------------------------------------------------------------+
|i8 : pushFwdF := pushFwd(f,F);                                               |
+-----------------------------------------------------------------------------+
|i9 : G := complete res M;                                                    |
+-----------------------------------------------------------------------------+
|i10 : E := spectralSequence(filteredComplex(G) ** pushFwdF);                 |
+-----------------------------------------------------------------------------+
|i11 : EE := spectralSequence(G ** (filteredComplex pushFwdF));               |
+-----------------------------------------------------------------------------+
|i12 : e = prune E;                                                           |
+-----------------------------------------------------------------------------+
|i13 : ee = prune EE;                                                         |
+-----------------------------------------------------------------------------+
|i14 : e^0                                                                    |
|                                                                             |
|      +------------------------------------+---------------------------------|
|o14 = |cokernel | 0  0  b2-ac |            |cokernel {1} | 0  0  0  0  0  0  |
|      |         | -c -b 0     |            |         {1} | -c -b 0  0  0  0  |
|      |         | b  a  0     |            |         {1} | b  a  0  0  0  0  |
|      |                                    |         {1} | 0  0  0  0  0  0  |
|      |{0, 2}                              |         {1} | 0  0  -c -b 0  0  |
|      |                                    |         {1} | 0  0  b  a  0  0  |
|      |                                    |         {1} | 0  0  0  0  0  0  |
|      |                                    |         {1} | 0  0  0  0  -c -b |
|      |                                    |         {1} | 0  0  0  0  b  a  |
|      |                                    |                                 |
|      |                                    |{1, 2}                           |
|      +------------------------------------+---------------------------------|
|      |cokernel | 0  0  0  0  b2-ac 0     ||cokernel {1} | 0  0  0  0  0  0  |
|      |         | 0  0  0  0  0     b2-ac ||         {1} | 0  0  0  0  0  0  |
|      |         | -c -b 0  0  0     0     ||         {1} | -c -b 0  0  0  0  |
|      |         | 0  0  -c -b 0     0     ||         {1} | 0  0  -c -b 0  0  |
|      |         | b  a  0  0  0     0     ||         {1} | b  a  0  0  0  0  |
|      |         | 0  0  b  a  0     0     ||         {1} | 0  0  b  a  0  0  |
|      |                                    |         {1} | 0  0  0  0  0  0  |
|      |{0, 1}                              |         {1} | 0  0  0  0  0  0  |
|      |                                    |         {1} | 0  0  0  0  -c -b |
|      |                                    |         {1} | 0  0  0  0  0  0  |
|      |                                    |         {1} | 0  0  0  0  b  a  |
|      |                                    |         {1} | 0  0  0  0  0  0  |
|      |                                    |         {1} | 0  0  0  0  0  0  |
|      |                                    |         {1} | 0  0  0  0  0  0  |
|      |                                    |         {1} | 0  0  0  0  0  0  |
|      |                                    |         {1} | 0  0  0  0  0  0  |
|      |                                    |         {1} | 0  0  0  0  0  0  |
|      |                                    |         {1} | 0  0  0  0  0  0  |
|      |                                    |                                 |
|      |                                    |{1, 1}                           |
|      +------------------------------------+---------------------------------|
|      |cokernel | 0  0  b2-ac |            |cokernel | 0  0  0  0  0  0  b2-a|
|      |         | -c -b 0     |            |         | -c -b 0  0  0  0  0   |
|      |         | b  a  0     |            |         | b  a  0  0  0  0  0   |
|      |                                    |         | 0  0  0  0  0  0  0   |
|      |{0, 0}                              |         | 0  0  -c -b 0  0  0   |
|      |                                    |         | 0  0  b  a  0  0  0   |
|      |                                    |         | 0  0  0  0  0  0  0   |
|      |                                    |         | 0  0  0  0  -c -b 0   |
|      |                                    |         | 0  0  0  0  b  a  0   |
|      |                                    |                                 |
|      |                                    |{1, 0}                           |
|      +------------------------------------+---------------------------------|
|                                                                             |
|o14 : SpectralSequencePage                                                   |
|-----------------------------------------------------------------------------|
|-------------------------------------------------------+---------------------|
|b2-ac 0     0     |                                    |cokernel {2} | 0  0  |
|0     0     0     |                                    |         {2} | -c -b |
|0     0     0     |                                    |         {2} | b  a  |
|0     b2-ac 0     |                                    |         {2} | 0  0  |
|0     0     0     |                                    |         {2} | 0  0  |
|0     0     0     |                                    |         {2} | 0  0  |
|0     0     b2-ac |                                    |         {2} | 0  0  |
|0     0     0     |                                    |         {2} | 0  0  |
|0     0     0     |                                    |         {2} | 0  0  |
|                                                       |                     |
|                                                       |{2, 2}               |
|-------------------------------------------------------+---------------------|
|0  0  0  0  0  0  b2-ac 0     0     0     0     0     ||cokernel {2} | 0  0  |
|0  0  0  0  0  0  0     b2-ac 0     0     0     0     ||         {2} | 0  0  |
|0  0  0  0  0  0  0     0     0     0     0     0     ||         {2} | -c -b |
|0  0  0  0  0  0  0     0     0     0     0     0     ||         {2} | 0  0  |
|0  0  0  0  0  0  0     0     0     0     0     0     ||         {2} | b  a  |
|0  0  0  0  0  0  0     0     0     0     0     0     ||         {2} | 0  0  |
|0  0  0  0  0  0  0     0     b2-ac 0     0     0     ||         {2} | 0  0  |
|0  0  0  0  0  0  0     0     0     b2-ac 0     0     ||         {2} | 0  0  |
|0  0  0  0  0  0  0     0     0     0     0     0     ||         {2} | 0  0  |
|-c -b 0  0  0  0  0     0     0     0     0     0     ||         {2} | 0  0  |
|0  0  0  0  0  0  0     0     0     0     0     0     ||         {2} | 0  0  |
|b  a  0  0  0  0  0     0     0     0     0     0     ||         {2} | 0  0  |
|0  0  0  0  0  0  0     0     0     0     b2-ac 0     ||         {2} | 0  0  |
|0  0  0  0  0  0  0     0     0     0     0     b2-ac ||         {2} | 0  0  |
|0  0  -c -b 0  0  0     0     0     0     0     0     ||         {2} | 0  0  |
|0  0  0  0  -c -b 0     0     0     0     0     0     ||         {2} | 0  0  |
|0  0  b  a  0  0  0     0     0     0     0     0     ||         {2} | 0  0  |
|0  0  0  0  b  a  0     0     0     0     0     0     ||         {2} | 0  0  |
|                                                       |                     |
|                                                       |{2, 1}               |
|-------------------------------------------------------+---------------------|
|c 0     0     |                                        |cokernel | 0  0  0  0|
|  0     0     |                                        |         | -c -b 0  0|
|  0     0     |                                        |         | b  a  0  0|
|  b2-ac 0     |                                        |         | 0  0  0  0|
|  0     0     |                                        |         | 0  0  -c -|
|  0     0     |                                        |         | 0  0  b  a|
|  0     b2-ac |                                        |         | 0  0  0  0|
|  0     0     |                                        |         | 0  0  0  0|
|  0     0     |                                        |         | 0  0  0  0|
|                                                       |                     |
|                                                       |{2, 0}               |
|-------------------------------------------------------+---------------------|
|-----------------------------------------------------------------------------|
|-------------------------------------------------------------------+---------|
|0  0  0  0  b2-ac 0     0     |                                    |cokernel |
|0  0  0  0  0     0     0     |                                    |         |
|0  0  0  0  0     0     0     |                                    |         |
|0  0  0  0  0     b2-ac 0     |                                    |         |
|-c -b 0  0  0     0     0     |                                    |{3, 2}   |
|b  a  0  0  0     0     0     |                                    |         |
|0  0  0  0  0     0     b2-ac |                                    |         |
|0  0  -c -b 0     0     0     |                                    |         |
|0  0  b  a  0     0     0     |                                    |         |
|                                                                   |         |
|                                                                   |         |
|-------------------------------------------------------------------+---------|
|0  0  0  0  0  0  0  0  0  0  b2-ac 0     0     0     0     0     ||cokernel |
|0  0  0  0  0  0  0  0  0  0  0     b2-ac 0     0     0     0     ||         |
|0  0  0  0  0  0  0  0  0  0  0     0     0     0     0     0     ||         |
|-c -b 0  0  0  0  0  0  0  0  0     0     0     0     0     0     ||         |
|0  0  0  0  0  0  0  0  0  0  0     0     0     0     0     0     ||         |
|b  a  0  0  0  0  0  0  0  0  0     0     0     0     0     0     ||         |
|0  0  0  0  0  0  0  0  0  0  0     0     b2-ac 0     0     0     ||         |
|0  0  0  0  0  0  0  0  0  0  0     0     0     b2-ac 0     0     ||{3, 1}   |
|0  0  -c -b 0  0  0  0  0  0  0     0     0     0     0     0     ||         |
|0  0  0  0  -c -b 0  0  0  0  0     0     0     0     0     0     ||         |
|0  0  b  a  0  0  0  0  0  0  0     0     0     0     0     0     ||         |
|0  0  0  0  b  a  0  0  0  0  0     0     0     0     0     0     ||         |
|0  0  0  0  0  0  0  0  0  0  0     0     0     0     b2-ac 0     ||         |
|0  0  0  0  0  0  0  0  0  0  0     0     0     0     0     b2-ac ||         |
|0  0  0  0  0  0  -c -b 0  0  0     0     0     0     0     0     ||         |
|0  0  0  0  0  0  0  0  -c -b 0     0     0     0     0     0     ||         |
|0  0  0  0  0  0  b  a  0  0  0     0     0     0     0     0     ||         |
|0  0  0  0  0  0  0  0  b  a  0     0     0     0     0     0     ||         |
|                                                                   |         |
|                                                                   |         |
|-------------------------------------------------------------------+---------|
|  0  0  b2-ac 0     0     |                                        |cokernel |
|  0  0  0     0     0     |                                        |         |
|  0  0  0     0     0     |                                        |         |
|  0  0  0     b2-ac 0     |                                        |         |
|b 0  0  0     0     0     |                                        |{3, 0}   |
|  0  0  0     0     0     |                                        |         |
|  0  0  0     0     b2-ac |                                        |         |
|  -c -b 0     0     0     |                                        |         |
|  b  a  0     0     0     |                                        |         |
|                                                                   |         |
|                                                                   |         |
|-------------------------------------------------------------------+---------|
|-----------------------------------------------------------------------------|
|-------------------------------+                                             |
|{3} | 0  0  b2-ac |            |                                             |
|{3} | -c -b 0     |            |                                             |
|{3} | b  a  0     |            |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|-------------------------------+                                             |
|{3} | 0  0  0  0  b2-ac 0     ||                                             |
|{3} | 0  0  0  0  0     b2-ac ||                                             |
|{3} | -c -b 0  0  0     0     ||                                             |
|{3} | 0  0  -c -b 0     0     ||                                             |
|{3} | b  a  0  0  0     0     ||                                             |
|{3} | 0  0  b  a  0     0     ||                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|-------------------------------+                                             |
|| 0  0  b2-ac |                |                                             |
|| -c -b 0     |                |                                             |
|| b  a  0     |                |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|-------------------------------+                                             |
+-----------------------------------------------------------------------------+
|i15 : e^1                                                                    |
|                                                                             |
|      +------------------+------------------------------+--------------------|
|o15 = |cokernel | c b a ||cokernel | c b a 0 0 0 0 0 0 ||cokernel | c b a 0 0|
|      |                  |         | 0 0 0 c b a 0 0 0 ||         | 0 0 0 c b|
|      |{0, 0}            |         | 0 0 0 0 0 0 c b a ||         | 0 0 0 0 0|
|      |                  |                              |                    |
|      |                  |{1, 0}                        |{2, 0}              |
|      +------------------+------------------------------+--------------------|
|                                                                             |
|o15 : SpectralSequencePage                                                   |
|-----------------------------------------------------------------------------|
|----------+------------------+                                               |
| 0 0 0 0 ||cokernel | c b a ||                                               |
| a 0 0 0 ||                  |                                               |
| 0 c b a ||{3, 0}            |                                               |
|          |                  |                                               |
|          |                  |                                               |
|----------+------------------+                                               |
+-----------------------------------------------------------------------------+
|i16 : e^2                                                                    |
|                                                                             |
|      +------------------+------------------------------+--------------------|
|o16 = |cokernel | c b a ||cokernel | c b a 0 0 0 0 0 0 ||cokernel | c b a 0 0|
|      |                  |         | 0 0 0 c b a 0 0 0 ||         | 0 0 0 c b|
|      |{0, 0}            |         | 0 0 0 0 0 0 c b a ||         | 0 0 0 0 0|
|      |                  |                              |                    |
|      |                  |{1, 0}                        |{2, 0}              |
|      +------------------+------------------------------+--------------------|
|                                                                             |
|o16 : SpectralSequencePage                                                   |
|-----------------------------------------------------------------------------|
|----------+------------------+                                               |
| 0 0 0 0 ||cokernel | c b a ||                                               |
| a 0 0 0 ||                  |                                               |
| 0 c b a ||{3, 0}            |                                               |
|          |                  |                                               |
|          |                  |                                               |
|----------+------------------+                                               |
+-----------------------------------------------------------------------------+
|i17 : e^infinity                                                             |
|                                                                             |
|      +------------------+------------------------------+--------------------|
|o17 = |cokernel | c b a ||cokernel | c b a 0 0 0 0 0 0 ||cokernel | c b a 0 0|
|      |                  |         | 0 0 0 c b a 0 0 0 ||         | 0 0 0 c b|
|      |{0, 0}            |         | 0 0 0 0 0 0 c b a ||         | 0 0 0 0 0|
|      |                  |                              |                    |
|      |                  |{1, 0}                        |{2, 0}              |
|      +------------------+------------------------------+--------------------|
|                                                                             |
|o17 : Page                                                                   |
|-----------------------------------------------------------------------------|
|----------+------------------+                                               |
| 0 0 0 0 ||cokernel | c b a ||                                               |
| a 0 0 0 ||                  |                                               |
| 0 c b a ||{3, 0}            |                                               |
|          |                  |                                               |
|          |                  |                                               |
|----------+------------------+                                               |
+-----------------------------------------------------------------------------+
|i18 : ee^0                                                                   |
|                                                                             |
|      +----------------------------------------------------+-----------------|
|o18 = |cokernel {3} | 0  0  b2-ac |                        |cokernel {3} | 0 |
|      |         {3} | -c -b 0     |                        |         {3} | 0 |
|      |         {3} | b  a  0     |                        |         {3} | -c|
|      |                                                    |         {3} | 0 |
|      |{0, 3}                                              |         {3} | b |
|      |                                                    |         {3} | 0 |
|      |                                                    |                 |
|      |                                                    |{1, 3}           |
|      +----------------------------------------------------+-----------------|
|      |cokernel {2} | 0  0  0  0  0  0  b2-ac 0     0     ||cokernel {2} | 0 |
|      |         {2} | -c -b 0  0  0  0  0     0     0     ||         {2} | 0 |
|      |         {2} | b  a  0  0  0  0  0     0     0     ||         {2} | -c|
|      |         {2} | 0  0  0  0  0  0  0     b2-ac 0     ||         {2} | 0 |
|      |         {2} | 0  0  -c -b 0  0  0     0     0     ||         {2} | b |
|      |         {2} | 0  0  b  a  0  0  0     0     0     ||         {2} | 0 |
|      |         {2} | 0  0  0  0  0  0  0     0     b2-ac ||         {2} | 0 |
|      |         {2} | 0  0  0  0  -c -b 0     0     0     ||         {2} | 0 |
|      |         {2} | 0  0  0  0  b  a  0     0     0     ||         {2} | 0 |
|      |                                                    |         {2} | 0 |
|      |{0, 2}                                              |         {2} | 0 |
|      |                                                    |         {2} | 0 |
|      |                                                    |         {2} | 0 |
|      |                                                    |         {2} | 0 |
|      |                                                    |         {2} | 0 |
|      |                                                    |         {2} | 0 |
|      |                                                    |         {2} | 0 |
|      |                                                    |         {2} | 0 |
|      |                                                    |                 |
|      |                                                    |{1, 2}           |
|      +----------------------------------------------------+-----------------|
|      |cokernel {1} | 0  0  0  0  0  0  b2-ac 0     0     ||cokernel {1} | 0 |
|      |         {1} | -c -b 0  0  0  0  0     0     0     ||         {1} | 0 |
|      |         {1} | b  a  0  0  0  0  0     0     0     ||         {1} | -c|
|      |         {1} | 0  0  0  0  0  0  0     b2-ac 0     ||         {1} | 0 |
|      |         {1} | 0  0  -c -b 0  0  0     0     0     ||         {1} | b |
|      |         {1} | 0  0  b  a  0  0  0     0     0     ||         {1} | 0 |
|      |         {1} | 0  0  0  0  0  0  0     0     b2-ac ||         {1} | 0 |
|      |         {1} | 0  0  0  0  -c -b 0     0     0     ||         {1} | 0 |
|      |         {1} | 0  0  0  0  b  a  0     0     0     ||         {1} | 0 |
|      |                                                    |         {1} | 0 |
|      |{0, 1}                                              |         {1} | 0 |
|      |                                                    |         {1} | 0 |
|      |                                                    |         {1} | 0 |
|      |                                                    |         {1} | 0 |
|      |                                                    |         {1} | 0 |
|      |                                                    |         {1} | 0 |
|      |                                                    |         {1} | 0 |
|      |                                                    |         {1} | 0 |
|      |                                                    |                 |
|      |                                                    |{1, 1}           |
|      +----------------------------------------------------+-----------------|
|      |cokernel | 0  0  b2-ac |                            |cokernel | 0  0  |
|      |         | -c -b 0     |                            |         | 0  0  |
|      |         | b  a  0     |                            |         | -c -b |
|      |                                                    |         | 0  0  |
|      |{0, 0}                                              |         | b  a  |
|      |                                                    |         | 0  0  |
|      |                                                    |                 |
|      |                                                    |{1, 0}           |
|      +----------------------------------------------------+-----------------|
|                                                                             |
|o18 : SpectralSequencePage                                                   |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------+-----|
| 0  0  0  b2-ac 0     |                                                |coker|
| 0  0  0  0     b2-ac |                                                |     |
| -b 0  0  0     0     |                                                |     |
| 0  -c -b 0     0     |                                                |     |
| a  0  0  0     0     |                                                |{2, 3|
| 0  b  a  0     0     |                                                |     |
|                                                                       |     |
|                                                                       |     |
|-----------------------------------------------------------------------+-----|
| 0  0  0  0  0  0  0  0  0  0  0  b2-ac 0     0     0     0     0     ||coker|
| 0  0  0  0  0  0  0  0  0  0  0  0     b2-ac 0     0     0     0     ||     |
| -b 0  0  0  0  0  0  0  0  0  0  0     0     0     0     0     0     ||     |
| 0  -c -b 0  0  0  0  0  0  0  0  0     0     0     0     0     0     ||     |
| a  0  0  0  0  0  0  0  0  0  0  0     0     0     0     0     0     ||     |
| 0  b  a  0  0  0  0  0  0  0  0  0     0     0     0     0     0     ||     |
| 0  0  0  0  0  0  0  0  0  0  0  0     0     b2-ac 0     0     0     ||     |
| 0  0  0  0  0  0  0  0  0  0  0  0     0     0     b2-ac 0     0     ||     |
| 0  0  0  -c -b 0  0  0  0  0  0  0     0     0     0     0     0     ||     |
| 0  0  0  0  0  -c -b 0  0  0  0  0     0     0     0     0     0     ||     |
| 0  0  0  b  a  0  0  0  0  0  0  0     0     0     0     0     0     ||{2, 2|
| 0  0  0  0  0  b  a  0  0  0  0  0     0     0     0     0     0     ||     |
| 0  0  0  0  0  0  0  0  0  0  0  0     0     0     0     b2-ac 0     ||     |
| 0  0  0  0  0  0  0  0  0  0  0  0     0     0     0     0     b2-ac ||     |
| 0  0  0  0  0  0  0  -c -b 0  0  0     0     0     0     0     0     ||     |
| 0  0  0  0  0  0  0  0  0  -c -b 0     0     0     0     0     0     ||     |
| 0  0  0  0  0  0  0  b  a  0  0  0     0     0     0     0     0     ||     |
| 0  0  0  0  0  0  0  0  0  b  a  0     0     0     0     0     0     ||     |
|                                                                       |     |
|                                                                       |     |
|-----------------------------------------------------------------------+-----|
| 0  0  0  0  0  0  0  0  0  0  0  b2-ac 0     0     0     0     0     ||coker|
| 0  0  0  0  0  0  0  0  0  0  0  0     b2-ac 0     0     0     0     ||     |
| -b 0  0  0  0  0  0  0  0  0  0  0     0     0     0     0     0     ||     |
| 0  -c -b 0  0  0  0  0  0  0  0  0     0     0     0     0     0     ||     |
| a  0  0  0  0  0  0  0  0  0  0  0     0     0     0     0     0     ||     |
| 0  b  a  0  0  0  0  0  0  0  0  0     0     0     0     0     0     ||     |
| 0  0  0  0  0  0  0  0  0  0  0  0     0     b2-ac 0     0     0     ||     |
| 0  0  0  0  0  0  0  0  0  0  0  0     0     0     b2-ac 0     0     ||     |
| 0  0  0  -c -b 0  0  0  0  0  0  0     0     0     0     0     0     ||     |
| 0  0  0  0  0  -c -b 0  0  0  0  0     0     0     0     0     0     ||     |
| 0  0  0  b  a  0  0  0  0  0  0  0     0     0     0     0     0     ||{2, 1|
| 0  0  0  0  0  b  a  0  0  0  0  0     0     0     0     0     0     ||     |
| 0  0  0  0  0  0  0  0  0  0  0  0     0     0     0     b2-ac 0     ||     |
| 0  0  0  0  0  0  0  0  0  0  0  0     0     0     0     0     b2-ac ||     |
| 0  0  0  0  0  0  0  -c -b 0  0  0     0     0     0     0     0     ||     |
| 0  0  0  0  0  0  0  0  0  -c -b 0     0     0     0     0     0     ||     |
| 0  0  0  0  0  0  0  b  a  0  0  0     0     0     0     0     0     ||     |
| 0  0  0  0  0  0  0  0  0  b  a  0     0     0     0     0     0     ||     |
|                                                                       |     |
|                                                                       |     |
|-----------------------------------------------------------------------+-----|
|0  0  b2-ac 0     |                                                    |coker|
|0  0  0     b2-ac |                                                    |     |
|0  0  0     0     |                                                    |     |
|-c -b 0     0     |                                                    |     |
|0  0  0     0     |                                                    |{2, 0|
|b  a  0     0     |                                                    |     |
|                                                                       |     |
|                                                                       |     |
|-----------------------------------------------------------------------+-----|
|-----------------------------------------------------------------------------|
|-----------------------------------------------+                             |
|nel {3} | 0  0  b2-ac |                        |                             |
|    {3} | -c -b 0     |                        |                             |
|    {3} | b  a  0     |                        |                             |
|                                               |                             |
|}                                              |                             |
|                                               |                             |
|                                               |                             |
|                                               |                             |
|-----------------------------------------------+                             |
|nel {2} | 0  0  0  0  0  0  b2-ac 0     0     ||                             |
|    {2} | -c -b 0  0  0  0  0     0     0     ||                             |
|    {2} | b  a  0  0  0  0  0     0     0     ||                             |
|    {2} | 0  0  0  0  0  0  0     b2-ac 0     ||                             |
|    {2} | 0  0  -c -b 0  0  0     0     0     ||                             |
|    {2} | 0  0  b  a  0  0  0     0     0     ||                             |
|    {2} | 0  0  0  0  0  0  0     0     b2-ac ||                             |
|    {2} | 0  0  0  0  -c -b 0     0     0     ||                             |
|    {2} | 0  0  0  0  b  a  0     0     0     ||                             |
|                                               |                             |
|}                                              |                             |
|                                               |                             |
|                                               |                             |
|                                               |                             |
|                                               |                             |
|                                               |                             |
|                                               |                             |
|                                               |                             |
|                                               |                             |
|                                               |                             |
|-----------------------------------------------+                             |
|nel | 0  0  0  0  0  0  b2-ac 0     0     |    |                             |
|    | -c -b 0  0  0  0  0     0     0     |    |                             |
|    | b  a  0  0  0  0  0     0     0     |    |                             |
|    | 0  0  0  0  0  0  0     b2-ac 0     |    |                             |
|    | 0  0  -c -b 0  0  0     0     0     |    |                             |
|    | 0  0  b  a  0  0  0     0     0     |    |                             |
|    | 0  0  0  0  0  0  0     0     b2-ac |    |                             |
|    | 0  0  0  0  -c -b 0     0     0     |    |                             |
|    | 0  0  0  0  b  a  0     0     0     |    |                             |
|                                               |                             |
|}                                              |                             |
|                                               |                             |
|                                               |                             |
|                                               |                             |
|                                               |                             |
|                                               |                             |
|                                               |                             |
|                                               |                             |
|                                               |                             |
|                                               |                             |
|-----------------------------------------------+                             |
|nel | 0  0  b2-ac |                            |                             |
|    | -c -b 0     |                            |                             |
|    | b  a  0     |                            |                             |
|                                               |                             |
|}                                              |                             |
|                                               |                             |
|                                               |                             |
|                                               |                             |
|-----------------------------------------------+                             |
+-----------------------------------------------------------------------------+

See also
========

  * Filtrations and tensor product complexes
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2100:0.

Examples of filtered complexes and spectral sequences -- How to use this package
********************************************************************************

Here is a list of some examples which illustrate various parts of this package.

First examples which show how to use this package

$\bullet$ See How to make filtered complexes from chain complex maps,

$\bullet$ See Filtrations and tensor product complexes,

$\bullet$ See Filtrations and homomorphism complexes,

$\bullet$ See Filtered complexes and simplicial complexes,

$\bullet$ See I-adic filtrations of chain complexes and their spectral sequences,

More elaborate examples which illustrate this package

$\bullet$ See Computing the Serre Spectral Sequence associated to a Hopf Fibration,

$\bullet$ See Balancing Tor,

$\bullet$ See Spectral sequences and hypercohomology calculations,

$\bullet$ See Spectral sequences and connecting morphisms,

$\bullet$ See Spectral sequences and non-Koszul syzygies,

$\bullet$ See Seeing Cancellations,

$\bullet$ See A spectral sequence which fails to degenerate quickly,

$\bullet$ See Edge homomorphisms,

$\bullet$ See Examples of change of rings Spectral Sequences,

More easy topological examples

$\bullet$ See Identifying anti-podal points of the two sphere,

$\bullet$ See The fibration of the Klein Bottle over the sphere with fibers the sphere,

$\bullet$ See The trivial fibration over the sphere with fibers the sphere,

-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:1208:0.

expression(SpectralSequence)
****************************

  * Function: expression (Macaulay2Doc),

Ways to use this method:
========================

  * expression(SpectralSequence)
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2250:0.

Filtered complexes and simplicial complexes
*******************************************

We can make a filtered complex from a nested list of simplicial complexes:

+--------------------------------------------------------------------+
|i1 : A = QQ[x,y,z,w];                                               |
+--------------------------------------------------------------------+
|i2 : F2D = simplicialComplex {x*y*z, w*z};                          |
+--------------------------------------------------------------------+
|i3 : F1D = simplicialComplex {x*y, w};                              |
+--------------------------------------------------------------------+
|i4 : F0D = simplicialComplex {x,w};                                 |
+--------------------------------------------------------------------+
|i5 : K = filteredComplex{F2D, F1D, F0D}                             |
|                                                                    |
|o5 = -1 : image 0 <-- image 0 <-- image 0 <-- image 0               |
|                                                                    |
|          -1          0           1           2                     |
|                                                                    |
|     0 : image | 1 | <-- image | 1 0 | <-- image 0 <-- image 0      |
|                               | 0 0 |                              |
|         -1                    | 0 0 |     1           2            |
|                               | 0 1 |                              |
|                                                                    |
|                         0                                          |
|                                                                    |
|     1 : image | 1 | <-- image | 1 0 0 | <-- image | 1 | <-- image 0|
|                               | 0 1 0 |           | 0 |            |
|         -1                    | 0 0 0 |           | 0 |     2      |
|                               | 0 0 1 |           | 0 |            |
|                                                                    |
|                         0                   1                      |
|                                                                    |
|           1       4       4       1                                |
|     2 : QQ  <-- QQ  <-- QQ  <-- QQ                                 |
|                                                                    |
|         -1      0       1       2                                  |
|                                                                    |
|o5 : FilteredComplex                                                |
+--------------------------------------------------------------------+

The resulting spectral sequence takes the form:

+-------------------------------------------------+
|i6 : E = prune spectralSequence K;               |
+-------------------------------------------------+
|i7 : E^0                                         |
|                                                 |
|     +-------+-------+-------+                   |
|     |  2    |  1    |  1    |                   |
|o7 = |QQ     |QQ     |QQ     |                   |
|     |       |       |       |                   |
|     |{0, 0} |{1, 0} |{2, 0} |                   |
|     +-------+-------+-------+                   |
|     |  1    |  1    |  3    |                   |
|     |QQ     |QQ     |QQ     |                   |
|     |       |       |       |                   |
|     |{0, -1}|{1, -1}|{2, -1}|                   |
|     +-------+-------+-------+                   |
|     |       |       |  1    |                   |
|     |0      |0      |QQ     |                   |
|     |       |       |       |                   |
|     |{0, -2}|{1, -2}|{2, -2}|                   |
|     +-------+-------+-------+                   |
|                                                 |
|o7 : SpectralSequencePage                        |
+-------------------------------------------------+
|i8 : E^0 .dd                                     |
|                                                 |
|o8 = {-1, 0} : 0 <----- 0 : {-1, 1}              |
|                    0                            |
|                                                 |
|     {-1, 1} : 0 <----- 0 : {-1, 2}              |
|                    0                            |
|                                                 |
|     {-1, 2} : 0 <----- 0 : {-1, 3}              |
|                    0                            |
|                                                 |
|     {2, -4} : 0 <----- 0 : {2, -3}              |
|                    0                            |
|                                                 |
|                          1                      |
|     {2, -3} : 0 <----- QQ  : {2, -2}            |
|                    0                            |
|                                                 |
|                 1                    3          |
|     {2, -2} : QQ  <--------------- QQ  : {2, -1}|
|                      | -1 -1 1 |                |
|                                                 |
|                 3               1               |
|     {2, -1} : QQ  <---------- QQ  : {2, 0}      |
|                      | 1  |                     |
|                      | -1 |                     |
|                      | 0  |                     |
|                                                 |
|     {1, -3} : 0 <----- 0 : {1, -2}              |
|                    0                            |
|                                                 |
|                          1                      |
|     {1, -2} : 0 <----- QQ  : {1, -1}            |
|                    0                            |
|                                                 |
|                 1               1               |
|     {1, -1} : QQ  <---------- QQ  : {1, 0}      |
|                      | -1 |                     |
|                                                 |
|                1                                |
|     {1, 0} : QQ  <----- 0 : {1, 1}              |
|                     0                           |
|                                                 |
|                          1                      |
|     {0, -2} : 0 <----- QQ  : {0, -1}            |
|                    0                            |
|                                                 |
|                 1                  2            |
|     {0, -1} : QQ  <------------- QQ  : {0, 0}   |
|                      | -1 -1 |                  |
|                                                 |
|                2                                |
|     {0, 0} : QQ  <----- 0 : {0, 1}              |
|                     0                           |
|                                                 |
|     {0, 1} : 0 <----- 0 : {0, 2}                |
|                   0                             |
|                                                 |
|     {-1, -1} : 0 <----- 0 : {-1, 0}             |
|                     0                           |
|                                                 |
|o8 : SpectralSequencePageMap                     |
+-------------------------------------------------+
|i9 : E^1                                         |
|                                                 |
|     +-------+-------+-------+                   |
|     |  1    |       |       |                   |
|o9 = |QQ     |0      |0      |                   |
|     |       |       |       |                   |
|     |{0, 0} |{1, 0} |{2, 0} |                   |
|     +-------+-------+-------+                   |
|     |       |       |  1    |                   |
|     |0      |0      |QQ     |                   |
|     |       |       |       |                   |
|     |{0, -1}|{1, -1}|{2, -1}|                   |
|     +-------+-------+-------+                   |
|                                                 |
|o9 : SpectralSequencePage                        |
+-------------------------------------------------+
|i10 : E^1 .dd                                    |
|                                                 |
|o10 = {-2, 1} : 0 <----- 0 : {-1, 1}             |
|                     0                           |
|                                                 |
|      {-2, 2} : 0 <----- 0 : {-1, 2}             |
|                     0                           |
|                                                 |
|      {-2, 3} : 0 <----- 0 : {-1, 3}             |
|                     0                           |
|                                                 |
|      {1, -3} : 0 <----- 0 : {2, -3}             |
|                     0                           |
|                                                 |
|      {1, -2} : 0 <----- 0 : {2, -2}             |
|                     0                           |
|                                                 |
|                           1                     |
|      {1, -1} : 0 <----- QQ  : {2, -1}           |
|                     0                           |
|                                                 |
|      {1, 0} : 0 <----- 0 : {2, 0}               |
|                    0                            |
|                                                 |
|      {0, -2} : 0 <----- 0 : {1, -2}             |
|                     0                           |
|                                                 |
|      {0, -1} : 0 <----- 0 : {1, -1}             |
|                     0                           |
|                                                 |
|                 1                               |
|      {0, 0} : QQ  <----- 0 : {1, 0}             |
|                      0                          |
|                                                 |
|      {0, 1} : 0 <----- 0 : {1, 1}               |
|                    0                            |
|                                                 |
|      {-1, -1} : 0 <----- 0 : {0, -1}            |
|                      0                          |
|                                                 |
|                           1                     |
|      {-1, 0} : 0 <----- QQ  : {0, 0}            |
|                     0                           |
|                                                 |
|      {-1, 1} : 0 <----- 0 : {0, 1}              |
|                     0                           |
|                                                 |
|      {-1, 2} : 0 <----- 0 : {0, 2}              |
|                     0                           |
|                                                 |
|      {-2, 0} : 0 <----- 0 : {-1, 0}             |
|                     0                           |
|                                                 |
|o10 : SpectralSequencePageMap                    |
+-------------------------------------------------+
|i11 : E^2                                        |
|                                                 |
|      +-------+-------+-------+                  |
|      |  1    |       |       |                  |
|o11 = |QQ     |0      |0      |                  |
|      |       |       |       |                  |
|      |{0, 0} |{1, 0} |{2, 0} |                  |
|      +-------+-------+-------+                  |
|      |       |       |  1    |                  |
|      |0      |0      |QQ     |                  |
|      |       |       |       |                  |
|      |{0, -1}|{1, -1}|{2, -1}|                  |
|      +-------+-------+-------+                  |
|                                                 |
|o11 : SpectralSequencePage                       |
+-------------------------------------------------+
|i12 : E^2 .dd                                    |
|                                                 |
|o12 = {-3, 2} : 0 <----- 0 : {-1, 1}             |
|                     0                           |
|                                                 |
|      {-3, 3} : 0 <----- 0 : {-1, 2}             |
|                     0                           |
|                                                 |
|      {-3, 4} : 0 <----- 0 : {-1, 3}             |
|                     0                           |
|                                                 |
|      {0, -2} : 0 <----- 0 : {2, -3}             |
|                     0                           |
|                                                 |
|      {0, -1} : 0 <----- 0 : {2, -2}             |
|                     0                           |
|                                                 |
|                 1               1               |
|      {0, 0} : QQ  <---------- QQ  : {2, -1}     |
|                      | -1 |                     |
|                                                 |
|      {0, 1} : 0 <----- 0 : {2, 0}               |
|                    0                            |
|                                                 |
|      {-1, -1} : 0 <----- 0 : {1, -2}            |
|                      0                          |
|                                                 |
|      {-1, 0} : 0 <----- 0 : {1, -1}             |
|                     0                           |
|                                                 |
|      {-1, 1} : 0 <----- 0 : {1, 0}              |
|                     0                           |
|                                                 |
|      {-1, 2} : 0 <----- 0 : {1, 1}              |
|                     0                           |
|                                                 |
|      {-2, 0} : 0 <----- 0 : {0, -1}             |
|                     0                           |
|                                                 |
|                           1                     |
|      {-2, 1} : 0 <----- QQ  : {0, 0}            |
|                     0                           |
|                                                 |
|      {-2, 2} : 0 <----- 0 : {0, 1}              |
|                     0                           |
|                                                 |
|      {-2, 3} : 0 <----- 0 : {0, 2}              |
|                     0                           |
|                                                 |
|      {-3, 1} : 0 <----- 0 : {-1, 0}             |
|                     0                           |
|                                                 |
|o12 : SpectralSequencePageMap                    |
+-------------------------------------------------+
|i13 : E^infinity                                 |
|                                                 |
|o13 = ++                                         |
|      ++                                         |
|                                                 |
|o13 : Page                                       |
+-------------------------------------------------+

If we want the homology of the complex to be the non-reduced homology of the
simplicial complex we set the ReducedHomology option to false:

+--------------------------------------------------------------------+
|i14 : k = filteredComplex({F2D, F1D, F0D}, ReducedHomology => false)|
|                                                                    |
|o14 = -1 : image 0 <-- image 0 <-- image 0 <-- image 0              |
|                                                                    |
|           -1          0           1           2                    |
|                                                                    |
|      0 : image 0 <-- image | 1 0 | <-- image 0 <-- image 0         |
|                            | 0 0 |                                 |
|          -1                | 0 0 |     1           2               |
|                            | 0 1 |                                 |
|                                                                    |
|                      0                                             |
|                                                                    |
|      1 : image 0 <-- image | 1 0 0 | <-- image | 1 | <-- image 0   |
|                            | 0 1 0 |           | 0 |               |
|          -1                | 0 0 0 |           | 0 |     2         |
|                            | 0 0 1 |           | 0 |               |
|                                                                    |
|                      0                   1                         |
|                                                                    |
|                        4       4       1                           |
|      2 : image 0 <-- QQ  <-- QQ  <-- QQ                            |
|                                                                    |
|          -1          0       1       2                             |
|                                                                    |
|o14 : FilteredComplex                                               |
+--------------------------------------------------------------------+

The resulting spectral sequence takes the form:

+--------------------------------------------------+
|i15 : e = prune spectralSequence k;               |
+--------------------------------------------------+
|i16 : e^0                                         |
|                                                  |
|      +-------+-------+-------+                   |
|      |  2    |  1    |  1    |                   |
|o16 = |QQ     |QQ     |QQ     |                   |
|      |       |       |       |                   |
|      |{0, 0} |{1, 0} |{2, 0} |                   |
|      +-------+-------+-------+                   |
|      |       |  1    |  3    |                   |
|      |0      |QQ     |QQ     |                   |
|      |       |       |       |                   |
|      |{0, -1}|{1, -1}|{2, -1}|                   |
|      +-------+-------+-------+                   |
|      |       |       |  1    |                   |
|      |0      |0      |QQ     |                   |
|      |       |       |       |                   |
|      |{0, -2}|{1, -2}|{2, -2}|                   |
|      +-------+-------+-------+                   |
|                                                  |
|o16 : SpectralSequencePage                        |
+--------------------------------------------------+
|i17 : e^0 .dd                                     |
|                                                  |
|o17 = {-1, 0} : 0 <----- 0 : {-1, 1}              |
|                     0                            |
|                                                  |
|      {-1, 1} : 0 <----- 0 : {-1, 2}              |
|                     0                            |
|                                                  |
|      {-1, 2} : 0 <----- 0 : {-1, 3}              |
|                     0                            |
|                                                  |
|      {2, -4} : 0 <----- 0 : {2, -3}              |
|                     0                            |
|                                                  |
|                           1                      |
|      {2, -3} : 0 <----- QQ  : {2, -2}            |
|                     0                            |
|                                                  |
|                  1                    3          |
|      {2, -2} : QQ  <--------------- QQ  : {2, -1}|
|                       | -1 -1 1 |                |
|                                                  |
|                  3               1               |
|      {2, -1} : QQ  <---------- QQ  : {2, 0}      |
|                       | 1  |                     |
|                       | -1 |                     |
|                       | 0  |                     |
|                                                  |
|      {1, -3} : 0 <----- 0 : {1, -2}              |
|                     0                            |
|                                                  |
|                           1                      |
|      {1, -2} : 0 <----- QQ  : {1, -1}            |
|                     0                            |
|                                                  |
|                  1               1               |
|      {1, -1} : QQ  <---------- QQ  : {1, 0}      |
|                       | -1 |                     |
|                                                  |
|                 1                                |
|      {1, 0} : QQ  <----- 0 : {1, 1}              |
|                      0                           |
|                                                  |
|      {0, -2} : 0 <----- 0 : {0, -1}              |
|                     0                            |
|                                                  |
|                           2                      |
|      {0, -1} : 0 <----- QQ  : {0, 0}             |
|                     0                            |
|                                                  |
|                 2                                |
|      {0, 0} : QQ  <----- 0 : {0, 1}              |
|                      0                           |
|                                                  |
|      {0, 1} : 0 <----- 0 : {0, 2}                |
|                    0                             |
|                                                  |
|      {-1, -1} : 0 <----- 0 : {-1, 0}             |
|                      0                           |
|                                                  |
|o17 : SpectralSequencePageMap                     |
+--------------------------------------------------+
|i18 : e^1 .dd                                     |
|                                                  |
|o18 = {-2, 1} : 0 <----- 0 : {-1, 1}              |
|                     0                            |
|                                                  |
|      {-2, 2} : 0 <----- 0 : {-1, 2}              |
|                     0                            |
|                                                  |
|      {-2, 3} : 0 <----- 0 : {-1, 3}              |
|                     0                            |
|                                                  |
|      {1, -3} : 0 <----- 0 : {2, -3}              |
|                     0                            |
|                                                  |
|      {1, -2} : 0 <----- 0 : {2, -2}              |
|                     0                            |
|                                                  |
|                           1                      |
|      {1, -1} : 0 <----- QQ  : {2, -1}            |
|                     0                            |
|                                                  |
|      {1, 0} : 0 <----- 0 : {2, 0}                |
|                    0                             |
|                                                  |
|      {0, -2} : 0 <----- 0 : {1, -2}              |
|                     0                            |
|                                                  |
|      {0, -1} : 0 <----- 0 : {1, -1}              |
|                     0                            |
|                                                  |
|                 2                                |
|      {0, 0} : QQ  <----- 0 : {1, 0}              |
|                      0                           |
|                                                  |
|      {0, 1} : 0 <----- 0 : {1, 1}                |
|                    0                             |
|                                                  |
|      {-1, -1} : 0 <----- 0 : {0, -1}             |
|                      0                           |
|                                                  |
|                           2                      |
|      {-1, 0} : 0 <----- QQ  : {0, 0}             |
|                     0                            |
|                                                  |
|      {-1, 1} : 0 <----- 0 : {0, 1}               |
|                     0                            |
|                                                  |
|      {-1, 2} : 0 <----- 0 : {0, 2}               |
|                     0                            |
|                                                  |
|      {-2, 0} : 0 <----- 0 : {-1, 0}              |
|                     0                            |
|                                                  |
|o18 : SpectralSequencePageMap                     |
+--------------------------------------------------+
|i19 : e^2                                         |
|                                                  |
|      +-------+-------+-------+                   |
|      |  2    |       |       |                   |
|o19 = |QQ     |0      |0      |                   |
|      |       |       |       |                   |
|      |{0, 0} |{1, 0} |{2, 0} |                   |
|      +-------+-------+-------+                   |
|      |       |       |  1    |                   |
|      |0      |0      |QQ     |                   |
|      |       |       |       |                   |
|      |{0, -1}|{1, -1}|{2, -1}|                   |
|      +-------+-------+-------+                   |
|                                                  |
|o19 : SpectralSequencePage                        |
+--------------------------------------------------+
|i20 : e^2 .dd                                     |
|                                                  |
|o20 = {-3, 2} : 0 <----- 0 : {-1, 1}              |
|                     0                            |
|                                                  |
|      {-3, 3} : 0 <----- 0 : {-1, 2}              |
|                     0                            |
|                                                  |
|      {-3, 4} : 0 <----- 0 : {-1, 3}              |
|                     0                            |
|                                                  |
|      {0, -2} : 0 <----- 0 : {2, -3}              |
|                     0                            |
|                                                  |
|      {0, -1} : 0 <----- 0 : {2, -2}              |
|                     0                            |
|                                                  |
|                 2               1                |
|      {0, 0} : QQ  <---------- QQ  : {2, -1}      |
|                      | 1  |                      |
|                      | -1 |                      |
|                                                  |
|      {0, 1} : 0 <----- 0 : {2, 0}                |
|                    0                             |
|                                                  |
|      {-1, -1} : 0 <----- 0 : {1, -2}             |
|                      0                           |
|                                                  |
|      {-1, 0} : 0 <----- 0 : {1, -1}              |
|                     0                            |
|                                                  |
|      {-1, 1} : 0 <----- 0 : {1, 0}               |
|                     0                            |
|                                                  |
|      {-1, 2} : 0 <----- 0 : {1, 1}               |
|                     0                            |
|                                                  |
|      {-2, 0} : 0 <----- 0 : {0, -1}              |
|                     0                            |
|                                                  |
|                           2                      |
|      {-2, 1} : 0 <----- QQ  : {0, 0}             |
|                     0                            |
|                                                  |
|      {-2, 2} : 0 <----- 0 : {0, 1}               |
|                     0                            |
|                                                  |
|      {-2, 3} : 0 <----- 0 : {0, 2}               |
|                     0                            |
|                                                  |
|      {-3, 1} : 0 <----- 0 : {-1, 0}              |
|                     0                            |
|                                                  |
|o20 : SpectralSequencePageMap                     |
+--------------------------------------------------+
|i21 : e^infinity                                  |
|                                                  |
|      +------+                                    |
|      |  1   |                                    |
|o21 = |QQ    |                                    |
|      |      |                                    |
|      |{0, 0}|                                    |
|      +------+                                    |
|                                                  |
|o21 : Page                                        |
+--------------------------------------------------+

See also
========

  * How to make filtered complexes from chain complex maps
  * Filtrations and tensor product complexes
  * Filtrations and homomorphism complexes
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:1276:0.

filtered complexes and spectral sequences from simplicial complexes
*******************************************************************

To make a filtered complex from a list of simplicial complexes we first need to
make some simplicial complexes.

+-------------------------------------------------+
|i1 : R = QQ[x,y,z,w];                            |
+-------------------------------------------------+
|i2 : a = simplicialComplex {x*y*z, x*y, y*z, w*z}|
|                                                 |
|o2 = simplicialComplex | zw xyz |                |
|                                                 |
|o2 : SimplicialComplex                           |
+-------------------------------------------------+
|i3 : b = simplicialComplex {x*y, w}              |
|                                                 |
|o3 = simplicialComplex | w xy |                  |
|                                                 |
|o3 : SimplicialComplex                           |
+-------------------------------------------------+
|i4 : c = simplicialComplex {x,w}                 |
|                                                 |
|o4 = simplicialComplex | w x |                   |
|                                                 |
|o4 : SimplicialComplex                           |
+-------------------------------------------------+

Note that $b$ is a simplicial subcomplex of $a$ and that $c$ is a simplicial
subcomplex of $b$. Let's now create a filtered complex.

+--------------------------------------------------------------------+
|i5 : K = filteredComplex{a,b,c}                                     |
|                                                                    |
|o5 = -1 : image 0 <-- image 0 <-- image 0 <-- image 0               |
|                                                                    |
|          -1          0           1           2                     |
|                                                                    |
|     0 : image | 1 | <-- image | 1 0 | <-- image 0 <-- image 0      |
|                               | 0 0 |                              |
|         -1                    | 0 0 |     1           2            |
|                               | 0 1 |                              |
|                                                                    |
|                         0                                          |
|                                                                    |
|     1 : image | 1 | <-- image | 1 0 0 | <-- image | 1 | <-- image 0|
|                               | 0 1 0 |           | 0 |            |
|         -1                    | 0 0 0 |           | 0 |     2      |
|                               | 0 0 1 |           | 0 |            |
|                                                                    |
|                         0                   1                      |
|                                                                    |
|           1       4       4       1                                |
|     2 : QQ  <-- QQ  <-- QQ  <-- QQ                                 |
|                                                                    |
|         -1      0       1       2                                  |
|                                                                    |
|o5 : FilteredComplex                                                |
+--------------------------------------------------------------------+

The associated spectral sequence takes the form:

+---------------------------+
|i6 : E = spectralSequence K|
|                           |
|o6 = E                     |
|                           |
|o6 : SpectralSequence      |
+---------------------------+

Let's view some pages and maps of these pages.

+-----------------------------------------------------------------------------+
|i7 : E^0                                                                     |
|                                                                             |
|     +-----------------------------+----------------------------------------+|
|     |                             |                                        ||
|o7 = |image | 1 0 0 0 0 0 0 0 0 0 ||image | 1 |                             ||
|     |      | 0 0 0 0 0 0 0 0 0 0 ||      | 0 |                             ||
|     |      | 0 0 0 0 0 0 0 0 0 0 ||      | 0 |                             ||
|     |      | 0 1 0 0 0 0 0 0 0 0 ||      | 0 |                             ||
|     |                             |                                        ||
|     |{0, 0}                       |{1, 0}                                  ||
|     +-----------------------------+----------------------------------------+|
|     |image | 1 0 0 0 0 0 |        |subquotient (| 1 0 0 1 0 |, | 1 0 |)    ||
|     |                             |             | 0 1 0 0 0 |  | 0 0 |     ||
|     |{0, -1}                      |             | 0 0 0 0 0 |  | 0 0 |     ||
|     |                             |             | 0 0 1 0 1 |  | 0 1 |     ||
|     |                             |                                        ||
|     |                             |{1, -1}                                 ||
|     +-----------------------------+----------------------------------------+|
|     |0                            |subquotient (| 1 -1 -1 1 |, | -1 -1 1 |)||
|     |                             |                                        ||
|     |{0, -2}                      |{1, -2}                                 ||
|     |                             |                                        ||
|     |                             |                                        ||
|     |                             |                                        ||
|     +-----------------------------+----------------------------------------+|
|                                                                             |
|o7 : SpectralSequencePage                                                    |
|-----------------------------------------------------------------------------|
|---------------------+                                                       |
|  1                  |                                                       |
|QQ                   |                                                       |
|                     |                                                       |
|{2, 0}               |                                                       |
|                     |                                                       |
|                     |                                                       |
|                     |                                                       |
|---------------------+                                                       |
|cokernel | 1 |       |                                                       |
|         | 0 |       |                                                       |
|         | 0 |       |                                                       |
|         | 0 |       |                                                       |
|                     |                                                       |
|{2, -1}              |                                                       |
|---------------------+                                                       |
|cokernel | 1  1 0 0 ||                                                       |
|         | -1 0 1 0 ||                                                       |
|         | 0  0 0 0 ||                                                       |
|         | 0  0 0 1 ||                                                       |
|                     |                                                       |
|{2, -2}              |                                                       |
|---------------------+                                                       |
+-----------------------------------------------------------------------------+
|i8 : F0 = minimalPresentation(E^0)                                           |
|                                                                             |
|     +-------+-------+-------+                                               |
|     |  2    |  1    |  1    |                                               |
|o8 = |QQ     |QQ     |QQ     |                                               |
|     |       |       |       |                                               |
|     |{0, 0} |{1, 0} |{2, 0} |                                               |
|     +-------+-------+-------+                                               |
|     |  1    |  1    |  3    |                                               |
|     |QQ     |QQ     |QQ     |                                               |
|     |       |       |       |                                               |
|     |{0, -1}|{1, -1}|{2, -1}|                                               |
|     +-------+-------+-------+                                               |
|     |       |       |  1    |                                               |
|     |0      |0      |QQ     |                                               |
|     |       |       |       |                                               |
|     |{0, -2}|{1, -2}|{2, -2}|                                               |
|     +-------+-------+-------+                                               |
|                                                                             |
|o8 : SpectralSequencePage                                                    |
+-----------------------------------------------------------------------------+
|i9 : E^0 .dd                                                                 |
|                                                                             |
|o9 = {-1, 0} : image 0 <----- image 0 : {-1, 1}                              |
|                          0                                                  |
|                                                                             |
|     {-1, 1} : image 0 <----- image 0 : {-1, 2}                              |
|                          0                                                  |
|                                                                             |
|     {-1, 2} : image 0 <----- image 0 : {-1, 3}                              |
|                          0                                                  |
|                                                                             |
|     {2, -4} : 0 <----- cokernel | -1 -1 -1 1 | : {2, -3}                    |
|                    0                                                        |
|                                                                             |
|     {2, -3} : cokernel | -1 -1 -1 1 | <----- cokernel | 1  1 0 0 | : {2, -2}|
|                                          0            | -1 0 1 0 |          |
|                                                       | 0  0 0 0 |          |
|                                                       | 0  0 0 1 |          |
|                                                                             |
|     {2, -2} : cokernel | 1  1 0 0 | <----------------- cokernel | 1 | : {2, |
|                        | -1 0 1 0 |    | 0 0  0  0 |            | 0 |       |
|                        | 0  0 0 0 |    | 0 0  0  0 |            | 0 |       |
|                        | 0  0 0 1 |    | 0 -1 -1 1 |            | 0 |       |
|                                        | 0 0  0  0 |                        |
|                                                                             |
|                                            1                                |
|     {2, -1} : cokernel | 1 | <---------- QQ  : {2, 0}                       |
|                        | 0 |    | 0  |                                      |
|                        | 0 |    | 1  |                                      |
|                        | 0 |    | -1 |                                      |
|                                 | 0  |                                      |
|                                                                             |
|     {1, -3} : 0 <----- subquotient (| 1 -1 -1 1 |, | -1 -1 1 |) : {1, -2}   |
|                    0                                                        |
|                                                                             |
|     {1, -2} : subquotient (| 1 -1 -1 1 |, | -1 -1 1 |) <----- subquotient (||
|                                                           0                ||
|                                                                            ||
|                                                                            ||
|                                                                             |
|     {1, -1} : subquotient (| 1 0 0 1 0 |, | 1 0 |) <---------- image | 1 | :|
|                            | 0 1 0 0 0 |  | 0 0 |     | 0  |         | 0 |  |
|                            | 0 0 0 0 0 |  | 0 0 |     | -1 |         | 0 |  |
|                            | 0 0 1 0 1 |  | 0 1 |     | 0  |         | 0 |  |
|                                                       | 0  |                |
|                                                       | 0  |                |
|                                                                             |
|     {1, 0} : image | 1 | <----- image 0 : {1, 1}                            |
|                    | 0 |    0                                               |
|                    | 0 |                                                    |
|                    | 0 |                                                    |
|                                                                             |
|     {0, -2} : 0 <----- image | 1 0 0 0 0 0 | : {0, -1}                      |
|                    0                                                        |
|                                                                             |
|     {0, -1} : image | 1 0 0 0 0 0 | <----------------------------- image | 1|
|                                        | -1 -1 0 0 0 0 0 0 0 0 |         | 0|
|                                        | 0  0  0 0 0 0 0 0 0 0 |         | 0|
|                                        | 0  0  0 0 0 0 0 0 0 0 |         | 0|
|                                        | 0  0  0 0 0 0 0 0 0 0 |            |
|                                        | 0  0  0 0 0 0 0 0 0 0 |            |
|                                        | 0  0  0 0 0 0 0 0 0 0 |            |
|                                                                             |
|     {0, 0} : image | 1 0 0 0 0 0 0 0 0 0 | <----- image 0 : {0, 1}          |
|                    | 0 0 0 0 0 0 0 0 0 0 |    0                             |
|                    | 0 0 0 0 0 0 0 0 0 0 |                                  |
|                    | 0 1 0 0 0 0 0 0 0 0 |                                  |
|                                                                             |
|     {0, 1} : image 0 <----- image 0 : {0, 2}                                |
|                         0                                                   |
|                                                                             |
|     {-1, -1} : 0 <----- image 0 : {-1, 0}                                   |
|                     0                                                       |
|                                                                             |
|o9 : SpectralSequencePageMap                                                 |
|-----------------------------------------------------------------------------|
|-1}                                                                          |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 1 0 0 1 0 |, | 1 0 |) : {1, -1}                                             |
| 0 1 0 0 0 |  | 0 0 |                                                        |
| 0 0 0 0 0 |  | 0 0 |                                                        |
| 0 0 1 0 1 |  | 0 1 |                                                        |
|                                                                             |
| {1, 0}                                                                      |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0 0 0 0 0 0 0 0 0 | : {0, 0}                                                |
| 0 0 0 0 0 0 0 0 0 |                                                         |
| 0 0 0 0 0 0 0 0 0 |                                                         |
| 1 0 0 0 0 0 0 0 0 |                                                         |
+-----------------------------------------------------------------------------+
|i10 : F0.dd                                                                  |
|                                                                             |
|o10 = {-1, 0} : 0 <----- 0 : {-1, 1}                                         |
|                     0                                                       |
|                                                                             |
|      {-1, 1} : 0 <----- 0 : {-1, 2}                                         |
|                     0                                                       |
|                                                                             |
|      {-1, 2} : 0 <----- 0 : {-1, 3}                                         |
|                     0                                                       |
|                                                                             |
|      {2, -4} : 0 <----- 0 : {2, -3}                                         |
|                     0                                                       |
|                                                                             |
|                           1                                                 |
|      {2, -3} : 0 <----- QQ  : {2, -2}                                       |
|                     0                                                       |
|                                                                             |
|                  1                    3                                     |
|      {2, -2} : QQ  <--------------- QQ  : {2, -1}                           |
|                       | -1 -1 1 |                                           |
|                                                                             |
|                  3               1                                          |
|      {2, -1} : QQ  <---------- QQ  : {2, 0}                                 |
|                       | 1  |                                                |
|                       | -1 |                                                |
|                       | 0  |                                                |
|                                                                             |
|      {1, -3} : 0 <----- 0 : {1, -2}                                         |
|                     0                                                       |
|                                                                             |
|                           1                                                 |
|      {1, -2} : 0 <----- QQ  : {1, -1}                                       |
|                     0                                                       |
|                                                                             |
|                  1               1                                          |
|      {1, -1} : QQ  <---------- QQ  : {1, 0}                                 |
|                       | -1 |                                                |
|                                                                             |
|                 1                                                           |
|      {1, 0} : QQ  <----- 0 : {1, 1}                                         |
|                      0                                                      |
|                                                                             |
|                           1                                                 |
|      {0, -2} : 0 <----- QQ  : {0, -1}                                       |
|                     0                                                       |
|                                                                             |
|                  1                  2                                       |
|      {0, -1} : QQ  <------------- QQ  : {0, 0}                              |
|                       | -1 -1 |                                             |
|                                                                             |
|                 2                                                           |
|      {0, 0} : QQ  <----- 0 : {0, 1}                                         |
|                      0                                                      |
|                                                                             |
|      {0, 1} : 0 <----- 0 : {0, 2}                                           |
|                    0                                                        |
|                                                                             |
|      {-1, -1} : 0 <----- 0 : {-1, 0}                                        |
|                      0                                                      |
|                                                                             |
|o10 : SpectralSequencePageMap                                                |
+-----------------------------------------------------------------------------+
|i11 : E^1                                                                    |
|                                                                             |
|      +----------------------------------------+-----------------------------|
|o11 = |image | -1 0 0 0 0 |                    |image 0                      |
|      |      | 0  0 0 0 0 |                    |                             |
|      |      | 0  0 0 0 0 |                    |{1, 0}                       |
|      |      | 1  0 0 0 0 |                    |                             |
|      |                                        |                             |
|      |{0, 0}                                  |                             |
|      +----------------------------------------+-----------------------------|
|      |subquotient (| 1 -1 -1 0 |, | -1 -1 0 |)|subquotient (| 1 0 0 1  1 0 ||
|      |                                        |             | 0 1 0 -1 0 0 ||
|      |{0, -1}                                 |             | 0 0 0 0  0 0 ||
|      |                                        |             | 0 0 1 0  0 1 ||
|      |                                        |                             |
|      |                                        |{1, -1}                      |
|      +----------------------------------------+-----------------------------|
|                                                                             |
|o11 : SpectralSequencePage                                                   |
|-----------------------------------------------------------------------------|
|-------------+---------------------------------------+                       |
|             |image 0                                |                       |
|             |                                       |                       |
|             |{2, 0}                                 |                       |
|             |                                       |                       |
|             |                                       |                       |
|             |                                       |                       |
|-------------+---------------------------------------+                       |
|, | 1  1 0 |)|subquotient (| 1 0  0 -1 1 |, | -1 1 |)|                       |
|  | -1 0 0 | |             | 0 -1 1 1  0 |  | 1  0 | |                       |
|  | 0  0 0 | |             | 0 1  0 -1 0 |  | -1 0 | |                       |
|  | 0  0 1 | |             | 0 0  1 0  0 |  | 0  0 | |                       |
|             |                                       |                       |
|             |{2, -1}                                |                       |
|-------------+---------------------------------------+                       |
+-----------------------------------------------------------------------------+
|i12 : F1 = minimalPresentation(E^1)                                          |
|                                                                             |
|      +-------+-------+-------+                                              |
|      |  1    |       |       |                                              |
|o12 = |QQ     |0      |0      |                                              |
|      |       |       |       |                                              |
|      |{0, 0} |{1, 0} |{2, 0} |                                              |
|      +-------+-------+-------+                                              |
|      |       |       |  1    |                                              |
|      |0      |0      |QQ     |                                              |
|      |       |       |       |                                              |
|      |{0, -1}|{1, -1}|{2, -1}|                                              |
|      +-------+-------+-------+                                              |
|                                                                             |
|o12 : SpectralSequencePage                                                   |
+-----------------------------------------------------------------------------+
|i13 : E^1 .dd                                                                |
|                                                                             |
|o13 = {-2, 1} : image 0 <----- image 0 : {-1, 1}                             |
|                           0                                                 |
|                                                                             |
|      {-2, 2} : image 0 <----- image 0 : {-1, 2}                             |
|                           0                                                 |
|                                                                             |
|      {-2, 3} : image 0 <----- image 0 : {-1, 3}                             |
|                           0                                                 |
|                                                                             |
|      {1, -3} : 0 <----- cokernel | -1 -1 -1 -1 1 | : {2                     |
|                     0                                                       |
|                                                                             |
|      {1, -2} : subquotient (| 1 -1 -1 -1 1 |, | -1 -1 -                     |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|      {1, -1} : subquotient (| 1 0 0 1  1 0 |, | 1  1 0                      |
|                             | 0 1 0 -1 0 0 |  | -1 0 0                      |
|                             | 0 0 0 0  0 0 |  | 0  0 0                      |
|                             | 0 0 1 0  0 1 |  | 0  0 1                      |
|                                                                             |
|      {1, 0} : image 0 <----- image 0 : {2, 0}                               |
|                          0                                                  |
|                                                                             |
|      {0, -2} : 0 <----- subquotient (| 1 -1 -1 -1 1 |,                      |
|                     0                                                       |
|                                                                             |
|      {0, -1} : subquotient (| 1 -1 -1 0 |, | -1 -1 0 |)                     |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|      {0, 0} : image | -1 0 0 0 0 | <----- image 0 : {1,                     |
|                     | 0  0 0 0 0 |    0                                     |
|                     | 0  0 0 0 0 |                                          |
|                     | 1  0 0 0 0 |                                          |
|                                                                             |
|      {0, 1} : image 0 <----- image 0 : {1, 1}                               |
|                          0                                                  |
|                                                                             |
|      {-1, -1} : 0 <----- subquotient (| 1 -1 -1 0 |, |                      |
|                      0                                                      |
|                                                                             |
|      {-1, 0} : image 0 <----- image | -1 0 0 0 0 | : {0                     |
|                           0         | 0  0 0 0 0 |                          |
|                                     | 0  0 0 0 0 |                          |
|                                     | 1  0 0 0 0 |                          |
|                                                                             |
|      {-1, 1} : image 0 <----- image 0 : {0, 1}                              |
|                           0                                                 |
|                                                                             |
|      {-1, 2} : image 0 <----- image 0 : {0, 2}                              |
|                           0                                                 |
|                                                                             |
|      {-2, 0} : 0 <----- image 0 : {-1, 0}                                   |
|                     0                                                       |
|                                                                             |
|o13 : SpectralSequencePageMap                                                |
|-----------------------------------------------------------------------------|
|, -3}                                                                        |
|                                                                             |
|                                                                             |
|1 1 |) <----- cokernel | 1  1  0  0  1 0 0 | : {2, -2}                       |
|          0            | -1 0  1  0  0 1 0 |                                 |
|                       | 0  -1 -1 1  0 0 0 |                                 |
|                       | 0  0  0  -1 0 0 1 |                                 |
|                                                                             |
||) <----- subquotient (| 1 0  0 -1 1 |, | -1 1 |) : {2, -1}                  |
||     0                | 0 -1 1 1  0 |  | 1  0 |                             |
||                      | 0 1  0 -1 0 |  | -1 0 |                             |
||                      | 0 0  1 0  0 |  | 0  0 |                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|| -1 -1 -1 1 |) : {1, -2}                                                    |
|                                                                             |
|                                                                             |
| <----- subquotient (| 1 0 0 1  1 0 |, | 1  1 0 |) : {1, -1}                 |
|    0                | 0 1 0 -1 0 0 |  | -1 0 0 |                            |
|                     | 0 0 0 0  0 0 |  | 0  0 0 |                            |
|                     | 0 0 1 0  0 1 |  | 0  0 1 |                            |
|                                                                             |
| 0}                                                                          |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-1 -1 0 |) : {0, -1}                                                         |
|                                                                             |
|                                                                             |
|, 0}                                                                         |
+-----------------------------------------------------------------------------+
|i14 : F1.dd                                                                  |
|                                                                             |
|o14 = {-2, 1} : 0 <----- 0 : {-1, 1}                                         |
|                     0                                                       |
|                                                                             |
|      {-2, 2} : 0 <----- 0 : {-1, 2}                                         |
|                     0                                                       |
|                                                                             |
|      {-2, 3} : 0 <----- 0 : {-1, 3}                                         |
|                     0                                                       |
|                                                                             |
|      {1, -3} : 0 <----- 0 : {2, -3}                                         |
|                     0                                                       |
|                                                                             |
|      {1, -2} : 0 <----- 0 : {2, -2}                                         |
|                     0                                                       |
|                                                                             |
|                           1                                                 |
|      {1, -1} : 0 <----- QQ  : {2, -1}                                       |
|                     0                                                       |
|                                                                             |
|      {1, 0} : 0 <----- 0 : {2, 0}                                           |
|                    0                                                        |
|                                                                             |
|      {0, -2} : 0 <----- 0 : {1, -2}                                         |
|                     0                                                       |
|                                                                             |
|      {0, -1} : 0 <----- 0 : {1, -1}                                         |
|                     0                                                       |
|                                                                             |
|                 1                                                           |
|      {0, 0} : QQ  <----- 0 : {1, 0}                                         |
|                      0                                                      |
|                                                                             |
|      {0, 1} : 0 <----- 0 : {1, 1}                                           |
|                    0                                                        |
|                                                                             |
|      {-1, -1} : 0 <----- 0 : {0, -1}                                        |
|                      0                                                      |
|                                                                             |
|                           1                                                 |
|      {-1, 0} : 0 <----- QQ  : {0, 0}                                        |
|                     0                                                       |
|                                                                             |
|      {-1, 1} : 0 <----- 0 : {0, 1}                                          |
|                     0                                                       |
|                                                                             |
|      {-1, 2} : 0 <----- 0 : {0, 2}                                          |
|                     0                                                       |
|                                                                             |
|      {-2, 0} : 0 <----- 0 : {-1, 0}                                         |
|                     0                                                       |
|                                                                             |
|o14 : SpectralSequencePageMap                                                |
+-----------------------------------------------------------------------------+
|i15 : E^2                                                                    |
|                                                                             |
|      +-----------------------------------------------+----------------------|
|o15 = |subquotient (| -1 1  0 0 0 0 |, | 1  0 0 0 0 |)|subquotient (| -1 |, ||
|      |             | 0  -1 0 0 0 0 |  | -1 0 0 0 0 | |             | 1  |  ||
|      |             | 0  0  0 0 0 0 |  | 0  0 0 0 0 | |             | -1 |  ||
|      |             | 1  0  0 0 0 0 |  | 0  0 0 0 0 | |             | 0  |  ||
|      |                                               |                      |
|      |{0, 0}                                         |{1, 0}                |
|      +-----------------------------------------------+----------------------|
|      |subquotient (| 1 -1 -1 -1 0 |, | -1 -1 -1 0 |) |subquotient (| -1 -1 1|
|      |                                               |             | 1  0  -|
|      |{0, -1}                                        |             | 0  0  0|
|      |                                               |             | 0  1  0|
|      |                                               |                      |
|      |                                               |{1, -1}               |
|      +-----------------------------------------------+----------------------|
|                                                                             |
|o15 : SpectralSequencePage                                                   |
|-----------------------------------------------------------------------------|
|--------------------------------------+-------------------------------------+|
| -1 |)                                |image 0                              ||
| 1  |                                 |                                     ||
| -1 |                                 |{2, 0}                               ||
| 0  |                                 |                                     ||
|                                      |                                     ||
|                                      |                                     ||
|--------------------------------------+-------------------------------------+|
|  1  0  0  1 0 |, | 1  1  0  0  1 0 |)|subquotient (| 1  0 -1 1 |, | -1 1 |)||
|1 0  1  0  0 0 |  | -1 0  1  0  0 0 | |             | -1 1 1  0 |  | 1  0 | ||
|  -1 -1 1  0 0 |  | 0  -1 -1 1  0 0 | |             | 1  0 -1 0 |  | -1 0 | ||
|  0  0  -1 0 1 |  | 0  0  0  -1 0 1 | |             | 0  1 0  0 |  | 0  0 | ||
|                                      |                                     ||
|                                      |{2, -1}                              ||
|--------------------------------------+-------------------------------------+|
+-----------------------------------------------------------------------------+
|i16 : F2 = minimalPresentation(E^2)                                          |
|                                                                             |
|      +-------+-------+-------+                                              |
|      |  1    |       |       |                                              |
|o16 = |QQ     |0      |0      |                                              |
|      |       |       |       |                                              |
|      |{0, 0} |{1, 0} |{2, 0} |                                              |
|      +-------+-------+-------+                                              |
|      |       |       |  1    |                                              |
|      |0      |0      |QQ     |                                              |
|      |       |       |       |                                              |
|      |{0, -1}|{1, -1}|{2, -1}|                                              |
|      +-------+-------+-------+                                              |
|                                                                             |
|o16 : SpectralSequencePage                                                   |
+-----------------------------------------------------------------------------+
|i17 : E^2 .dd                                                                |
|                                                                             |
|o17 = {-3, 2} : image 0 <----- image 0 : {-1, 1}                             |
|                           0                                                 |
|                                                                             |
|      {-3, 3} : image 0 <----- image 0 : {-1, 2}                             |
|                           0                                                 |
|                                                                             |
|      {-3, 4} : image 0 <----- image 0 : {-1, 3}                             |
|                           0                                                 |
|                                                                             |
|      {0, -2} : 0 <----- cokernel | -1 -1 -1 -1 1 | : {2, -3}                |
|                     0                                                       |
|                                                                             |
|      {0, -1} : subquotient (| 1 -1 -1 -1 0 |, | -1 -1 -1 0 |)               |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|      {0, 0} : subquotient (| -1 1  0 0 0 0 |, | 1  0 0 0 0 |)               |
|                            | 0  -1 0 0 0 0 |  | -1 0 0 0 0 |                |
|                            | 0  0  0 0 0 0 |  | 0  0 0 0 0 |                |
|                            | 1  0  0 0 0 0 |  | 0  0 0 0 0 |                |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|      {0, 1} : image 0 <----- image 0 : {2, 0}                               |
|                          0                                                  |
|                                                                             |
|      {-1, -1} : 0 <----- subquotient (| 1 -1 -1 -1 -1 1 |, | -              |
|                      0                                                      |
|                                                                             |
|      {-1, 0} : subquotient (| 0 -1 -1 0 |, | -1 -1 0 |) <-----              |
|                                                            0                |
|                                                                             |
|                                                                             |
|                                                                             |
|      {-1, 1} : image 0 <----- subquotient (| -1 |, | -1 |) : {              |
|                           0                | 1  |  | 1  |                   |
|                                            | -1 |  | -1 |                   |
|                                            | 0  |  | 0  |                   |
|                                                                             |
|      {-1, 2} : image 0 <----- image 0 : {1, 1}                              |
|                           0                                                 |
|                                                                             |
|      {-2, 0} : 0 <----- subquotient (| 1 -1 -1 -1 0 |, | -1 -1              |
|                     0                                                       |
|                                                                             |
|      {-2, 1} : image 0 <----- subquotient (| -1 1  0 0 0 0 |,               |
|                           0                | 0  -1 0 0 0 0 |                |
|                                            | 0  0  0 0 0 0 |                |
|                                            | 1  0  0 0 0 0 |                |
|                                                                             |
|      {-2, 2} : image 0 <----- image 0 : {0, 1}                              |
|                           0                                                 |
|                                                                             |
|      {-2, 3} : image 0 <----- image 0 : {0, 2}                              |
|                           0                                                 |
|                                                                             |
|      {-3, 1} : 0 <----- subquotient (| 0 -1 -1 0 |, | -1 -1 0               |
|                     0                                                       |
|                                                                             |
|o17 : SpectralSequencePageMap                                                |
|-----------------------------------------------------------------------------|
|<----- cokernel | 1  1  0  0  1 0 0 | : {2, -2}                              |
|   0            | -1 0  1  0  0 1 0 |                                        |
|                | 0  -1 -1 1  0 0 0 |                                        |
|                | 0  0  0  -1 0 0 1 |                                        |
|                                                                             |
|<---------------- subquotient (| 1  0 -1 1 |, | -1 1 |) : {2, -1}            |
|   | 0 -1 0 0 |                | -1 1 1  0 |  | 1  0 |                       |
|   | 0 0  0 0 |                | 1  0 -1 0 |  | -1 0 |                       |
|   | 0 0  0 0 |                | 0  1 0  0 |  | 0  0 |                       |
|   | 0 0  0 0 |                                                              |
|   | 0 0  0 0 |                                                              |
|   | 0 0  0 0 |                                                              |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|1 -1 -1 -1 1 |) : {1, -2}                                                    |
|                                                                             |
|                                                                             |
| subquotient (| -1 -1 1  1  0  0  1 0 |, | 1  1  0  0  1 0 |) : {1, -1}      |
|              | 1  0  -1 0  1  0  0 0 |  | -1 0  1  0  0 0 |                 |
|              | 0  0  0  -1 -1 1  0 0 |  | 0  -1 -1 1  0 0 |                 |
|              | 0  1  0  0  0  -1 0 1 |  | 0  0  0  -1 0 1 |                 |
|                                                                             |
|1, 0}                                                                        |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| -1 0 |) : {0, -1}                                                           |
|                                                                             |
|                                                                             |
|| 1  0 0 0 0 |) : {0, 0}                                                     |
|| -1 0 0 0 0 |                                                               |
|| 0  0 0 0 0 |                                                               |
|| 0  0 0 0 0 |                                                               |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
||) : {-1, 0}                                                                 |
+-----------------------------------------------------------------------------+
|i18 : F2.dd                                                                  |
|                                                                             |
|o18 = {-3, 2} : 0 <----- 0 : {-1, 1}                                         |
|                     0                                                       |
|                                                                             |
|      {-3, 3} : 0 <----- 0 : {-1, 2}                                         |
|                     0                                                       |
|                                                                             |
|      {-3, 4} : 0 <----- 0 : {-1, 3}                                         |
|                     0                                                       |
|                                                                             |
|      {0, -2} : 0 <----- 0 : {2, -3}                                         |
|                     0                                                       |
|                                                                             |
|      {0, -1} : 0 <----- 0 : {2, -2}                                         |
|                     0                                                       |
|                                                                             |
|                 1               1                                           |
|      {0, 0} : QQ  <---------- QQ  : {2, -1}                                 |
|                      | -1 |                                                 |
|                                                                             |
|      {0, 1} : 0 <----- 0 : {2, 0}                                           |
|                    0                                                        |
|                                                                             |
|      {-1, -1} : 0 <----- 0 : {1, -2}                                        |
|                      0                                                      |
|                                                                             |
|      {-1, 0} : 0 <----- 0 : {1, -1}                                         |
|                     0                                                       |
|                                                                             |
|      {-1, 1} : 0 <----- 0 : {1, 0}                                          |
|                     0                                                       |
|                                                                             |
|      {-1, 2} : 0 <----- 0 : {1, 1}                                          |
|                     0                                                       |
|                                                                             |
|      {-2, 0} : 0 <----- 0 : {0, -1}                                         |
|                     0                                                       |
|                                                                             |
|                           1                                                 |
|      {-2, 1} : 0 <----- QQ  : {0, 0}                                        |
|                     0                                                       |
|                                                                             |
|      {-2, 2} : 0 <----- 0 : {0, 1}                                          |
|                     0                                                       |
|                                                                             |
|      {-2, 3} : 0 <----- 0 : {0, 2}                                          |
|                     0                                                       |
|                                                                             |
|      {-3, 1} : 0 <----- 0 : {-1, 0}                                         |
|                     0                                                       |
|                                                                             |
|o18 : SpectralSequencePageMap                                                |
+-----------------------------------------------------------------------------+
|i19 : E^infinity                                                             |
|                                                                             |
|o19 = ++                                                                     |
|      ++                                                                     |
|                                                                             |
|o19 : Page                                                                   |
+-----------------------------------------------------------------------------+
|i20 : (prune E) ^infinity                                                    |
|                                                                             |
|o20 = ++                                                                     |
|      ++                                                                     |
|                                                                             |
|o20 : Page                                                                   |
+-----------------------------------------------------------------------------+

If we want the resulting complexes to correspond to the non-reduced homology of
the simplicial complexes we set the ReducedHomology option to false.

+-----------------------------------------------------------------+
|i21 : J = filteredComplex({a,b,c}, ReducedHomology => false)     |
|                                                                 |
|o21 = -1 : image 0 <-- image 0 <-- image 0 <-- image 0           |
|                                                                 |
|           -1          0           1           2                 |
|                                                                 |
|      0 : image 0 <-- image | 1 0 | <-- image 0 <-- image 0      |
|                            | 0 0 |                              |
|          -1                | 0 0 |     1           2            |
|                            | 0 1 |                              |
|                                                                 |
|                      0                                          |
|                                                                 |
|      1 : image 0 <-- image | 1 0 0 | <-- image | 1 | <-- image 0|
|                            | 0 1 0 |           | 0 |            |
|          -1                | 0 0 0 |           | 0 |     2      |
|                            | 0 0 1 |           | 0 |            |
|                                                                 |
|                      0                   1                      |
|                                                                 |
|                        4       4       1                        |
|      2 : image 0 <-- QQ  <-- QQ  <-- QQ                         |
|                                                                 |
|          -1          0       1       2                          |
|                                                                 |
|o21 : FilteredComplex                                            |
+-----------------------------------------------------------------+

The resulting spectral sequence looks like

+-----------------------------------------------------------------------------+
|i22 : D = spectralSequence J                                                 |
|                                                                             |
|o22 = D                                                                      |
|                                                                             |
|o22 : SpectralSequence                                                       |
+-----------------------------------------------------------------------------+
|i23 : D^0                                                                    |
|                                                                             |
|      +-----------------------------+------------------------------------+---|
|      |                             |                                    |  1|
|o23 = |image | 1 0 0 0 0 0 0 0 0 0 ||image | 1 |                         |QQ |
|      |      | 0 0 0 0 0 0 0 0 0 0 ||      | 0 |                         |   |
|      |      | 0 0 0 0 0 0 0 0 0 0 ||      | 0 |                         |{2,|
|      |      | 0 1 0 0 0 0 0 0 0 0 ||      | 0 |                         |   |
|      |                             |                                    |   |
|      |{0, 0}                       |{1, 0}                              |   |
|      +-----------------------------+------------------------------------+---|
|      |image 0                      |subquotient (| 1 0 0 1 0 |, | 1 0 |)|cok|
|      |                             |             | 0 1 0 0 0 |  | 0 0 | |   |
|      |{0, -1}                      |             | 0 0 0 0 0 |  | 0 0 | |   |
|      |                             |             | 0 0 1 0 1 |  | 0 1 | |   |
|      |                             |                                    |   |
|      |                             |{1, -1}                             |{2,|
|      +-----------------------------+------------------------------------+---|
|      |0                            |image 0                             |cok|
|      |                             |                                    |   |
|      |{0, -2}                      |{1, -2}                             |   |
|      |                             |                                    |   |
|      |                             |                                    |   |
|      |                             |                                    |{2,|
|      +-----------------------------+------------------------------------+---|
|                                                                             |
|o23 : SpectralSequencePage                                                   |
|-----------------------------------------------------------------------------|
|------------------+                                                          |
|                  |                                                          |
|                  |                                                          |
|                  |                                                          |
| 0}               |                                                          |
|                  |                                                          |
|                  |                                                          |
|                  |                                                          |
|------------------+                                                          |
|ernel | 1 |       |                                                          |
|      | 0 |       |                                                          |
|      | 0 |       |                                                          |
|      | 0 |       |                                                          |
|                  |                                                          |
| -1}              |                                                          |
|------------------+                                                          |
|ernel | 1  1 0 0 ||                                                          |
|      | -1 0 1 0 ||                                                          |
|      | 0  0 0 0 ||                                                          |
|      | 0  0 0 1 ||                                                          |
|                  |                                                          |
| -2}              |                                                          |
|------------------+                                                          |
+-----------------------------------------------------------------------------+
|i24 : G0 = minimalPresentation(D^0)                                          |
|                                                                             |
|      +-------+-------+-------+                                              |
|      |  2    |  1    |  1    |                                              |
|o24 = |QQ     |QQ     |QQ     |                                              |
|      |       |       |       |                                              |
|      |{0, 0} |{1, 0} |{2, 0} |                                              |
|      +-------+-------+-------+                                              |
|      |       |  1    |  3    |                                              |
|      |0      |QQ     |QQ     |                                              |
|      |       |       |       |                                              |
|      |{0, -1}|{1, -1}|{2, -1}|                                              |
|      +-------+-------+-------+                                              |
|      |       |       |  1    |                                              |
|      |0      |0      |QQ     |                                              |
|      |       |       |       |                                              |
|      |{0, -2}|{1, -2}|{2, -2}|                                              |
|      +-------+-------+-------+                                              |
|                                                                             |
|o24 : SpectralSequencePage                                                   |
+-----------------------------------------------------------------------------+
|i25 : G0.dd                                                                  |
|                                                                             |
|o25 = {-1, 0} : 0 <----- 0 : {-1, 1}                                         |
|                     0                                                       |
|                                                                             |
|      {-1, 1} : 0 <----- 0 : {-1, 2}                                         |
|                     0                                                       |
|                                                                             |
|      {-1, 2} : 0 <----- 0 : {-1, 3}                                         |
|                     0                                                       |
|                                                                             |
|      {2, -4} : 0 <----- 0 : {2, -3}                                         |
|                     0                                                       |
|                                                                             |
|                           1                                                 |
|      {2, -3} : 0 <----- QQ  : {2, -2}                                       |
|                     0                                                       |
|                                                                             |
|                  1                    3                                     |
|      {2, -2} : QQ  <--------------- QQ  : {2, -1}                           |
|                       | -1 -1 1 |                                           |
|                                                                             |
|                  3               1                                          |
|      {2, -1} : QQ  <---------- QQ  : {2, 0}                                 |
|                       | 1  |                                                |
|                       | -1 |                                                |
|                       | 0  |                                                |
|                                                                             |
|      {1, -3} : 0 <----- 0 : {1, -2}                                         |
|                     0                                                       |
|                                                                             |
|                           1                                                 |
|      {1, -2} : 0 <----- QQ  : {1, -1}                                       |
|                     0                                                       |
|                                                                             |
|                  1               1                                          |
|      {1, -1} : QQ  <---------- QQ  : {1, 0}                                 |
|                       | -1 |                                                |
|                                                                             |
|                 1                                                           |
|      {1, 0} : QQ  <----- 0 : {1, 1}                                         |
|                      0                                                      |
|                                                                             |
|      {0, -2} : 0 <----- 0 : {0, -1}                                         |
|                     0                                                       |
|                                                                             |
|                           2                                                 |
|      {0, -1} : 0 <----- QQ  : {0, 0}                                        |
|                     0                                                       |
|                                                                             |
|                 2                                                           |
|      {0, 0} : QQ  <----- 0 : {0, 1}                                         |
|                      0                                                      |
|                                                                             |
|      {0, 1} : 0 <----- 0 : {0, 2}                                           |
|                    0                                                        |
|                                                                             |
|      {-1, -1} : 0 <----- 0 : {-1, 0}                                        |
|                      0                                                      |
|                                                                             |
|o25 : SpectralSequencePageMap                                                |
+-----------------------------------------------------------------------------+
|i26 : D^1                                                                    |
|                                                                             |
|      +---------------------+------------------------------------------+-----|
|o26 = |image | 1 0 0 0 0 0 ||image 0                                   |image|
|      |      | 0 0 0 0 0 0 ||                                          |     |
|      |      | 0 0 0 0 0 0 ||{1, 0}                                    |{2, 0|
|      |      | 0 1 0 0 0 0 ||                                          |     |
|      |                     |                                          |     |
|      |{0, 0}               |                                          |     |
|      +---------------------+------------------------------------------+-----|
|      |image 0              |subquotient (| 1 0 0 1  1 0 |, | 1  1 0 |)|subqu|
|      |                     |             | 0 1 0 -1 0 0 |  | -1 0 0 | |     |
|      |{0, -1}              |             | 0 0 0 0  0 0 |  | 0  0 0 | |     |
|      |                     |             | 0 0 1 0  0 1 |  | 0  0 1 | |     |
|      |                     |                                          |     |
|      |                     |{1, -1}                                   |{2, -|
|      +---------------------+------------------------------------------+-----|
|                                                                             |
|o26 : SpectralSequencePage                                                   |
|-----------------------------------------------------------------------------|
|----------------------------------+                                          |
| 0                                |                                          |
|                                  |                                          |
|}                                 |                                          |
|                                  |                                          |
|                                  |                                          |
|                                  |                                          |
|----------------------------------+                                          |
|otient (| 1 0  0 -1 1 |, | -1 1 |)|                                          |
|        | 0 -1 1 1  0 |  | 1  0 | |                                          |
|        | 0 1  0 -1 0 |  | -1 0 | |                                          |
|        | 0 0  1 0  0 |  | 0  0 | |                                          |
|                                  |                                          |
|1}                                |                                          |
|----------------------------------+                                          |
+-----------------------------------------------------------------------------+
|i27 : G1 = minimalPresentation(D^1)                                          |
|                                                                             |
|      +-------+-------+-------+                                              |
|      |  2    |       |       |                                              |
|o27 = |QQ     |0      |0      |                                              |
|      |       |       |       |                                              |
|      |{0, 0} |{1, 0} |{2, 0} |                                              |
|      +-------+-------+-------+                                              |
|      |       |       |  1    |                                              |
|      |0      |0      |QQ     |                                              |
|      |       |       |       |                                              |
|      |{0, -1}|{1, -1}|{2, -1}|                                              |
|      +-------+-------+-------+                                              |
|                                                                             |
|o27 : SpectralSequencePage                                                   |
+-----------------------------------------------------------------------------+
|i28 : G1.dd                                                                  |
|                                                                             |
|o28 = {-2, 1} : 0 <----- 0 : {-1, 1}                                         |
|                     0                                                       |
|                                                                             |
|      {-2, 2} : 0 <----- 0 : {-1, 2}                                         |
|                     0                                                       |
|                                                                             |
|      {-2, 3} : 0 <----- 0 : {-1, 3}                                         |
|                     0                                                       |
|                                                                             |
|      {1, -3} : 0 <----- 0 : {2, -3}                                         |
|                     0                                                       |
|                                                                             |
|      {1, -2} : 0 <----- 0 : {2, -2}                                         |
|                     0                                                       |
|                                                                             |
|                           1                                                 |
|      {1, -1} : 0 <----- QQ  : {2, -1}                                       |
|                     0                                                       |
|                                                                             |
|      {1, 0} : 0 <----- 0 : {2, 0}                                           |
|                    0                                                        |
|                                                                             |
|      {0, -2} : 0 <----- 0 : {1, -2}                                         |
|                     0                                                       |
|                                                                             |
|      {0, -1} : 0 <----- 0 : {1, -1}                                         |
|                     0                                                       |
|                                                                             |
|                 2                                                           |
|      {0, 0} : QQ  <----- 0 : {1, 0}                                         |
|                      0                                                      |
|                                                                             |
|      {0, 1} : 0 <----- 0 : {1, 1}                                           |
|                    0                                                        |
|                                                                             |
|      {-1, -1} : 0 <----- 0 : {0, -1}                                        |
|                      0                                                      |
|                                                                             |
|                           2                                                 |
|      {-1, 0} : 0 <----- QQ  : {0, 0}                                        |
|                     0                                                       |
|                                                                             |
|      {-1, 1} : 0 <----- 0 : {0, 1}                                          |
|                     0                                                       |
|                                                                             |
|      {-1, 2} : 0 <----- 0 : {0, 2}                                          |
|                     0                                                       |
|                                                                             |
|      {-2, 0} : 0 <----- 0 : {-1, 0}                                         |
|                     0                                                       |
|                                                                             |
|o28 : SpectralSequencePageMap                                                |
+-----------------------------------------------------------------------------+
|i29 : D^2                                                                    |
|                                                                             |
|      +------------------------------------------------+---------------------|
|o29 = |subquotient (| 1 0 1  0 0 0 0 |, | 1  0 0 0 0 |)|subquotient (| -1 |, |
|      |             | 0 0 -1 0 0 0 0 |  | -1 0 0 0 0 | |             | 1  |  |
|      |             | 0 0 0  0 0 0 0 |  | 0  0 0 0 0 | |             | -1 |  |
|      |             | 0 1 0  0 0 0 0 |  | 0  0 0 0 0 | |             | 0  |  |
|      |                                                |                     |
|      |{0, 0}                                          |{1, 0}               |
|      +------------------------------------------------+---------------------|
|      |image 0                                         |subquotient (| 1 0 0 |
|      |                                                |             | 0 1 0 |
|      |{0, -1}                                         |             | 0 0 0 |
|      |                                                |             | 0 0 1 |
|      |                                                |                     |
|      |                                                |{1, -1}              |
|      +------------------------------------------------+---------------------|
|                                                                             |
|o29 : SpectralSequencePage                                                   |
|-----------------------------------------------------------------------------|
|---------------------------------------+-------------------------------------|
|| -1 |)                                |image 0                              |
|| 1  |                                 |                                     |
|| -1 |                                 |{2, 0}                               |
|| 0  |                                 |                                     |
|                                       |                                     |
|                                       |                                     |
|---------------------------------------+-------------------------------------|
|1  1  0  0  1 0 |, | 1  1  0  0  1 0 |)|subquotient (| 1  0 -1 1 |, | -1 1 |)|
|-1 0  1  0  0 0 |  | -1 0  1  0  0 0 | |             | -1 1 1  0 |  | 1  0 | |
|0  -1 -1 1  0 0 |  | 0  -1 -1 1  0 0 | |             | 1  0 -1 0 |  | -1 0 | |
|0  0  0  -1 0 1 |  | 0  0  0  -1 0 1 | |             | 0  1 0  0 |  | 0  0 | |
|                                       |                                     |
|                                       |{2, -1}                              |
|---------------------------------------+-------------------------------------|
|-----------------------------------------------------------------------------|
|+                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
|+                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
|+                                                                            |
+-----------------------------------------------------------------------------+
|i30 : G2 = minimalPresentation(D^2)                                          |
|                                                                             |
|      +-------+-------+-------+                                              |
|      |  2    |       |       |                                              |
|o30 = |QQ     |0      |0      |                                              |
|      |       |       |       |                                              |
|      |{0, 0} |{1, 0} |{2, 0} |                                              |
|      +-------+-------+-------+                                              |
|      |       |       |  1    |                                              |
|      |0      |0      |QQ     |                                              |
|      |       |       |       |                                              |
|      |{0, -1}|{1, -1}|{2, -1}|                                              |
|      +-------+-------+-------+                                              |
|                                                                             |
|o30 : SpectralSequencePage                                                   |
+-----------------------------------------------------------------------------+
|i31 : G2.dd                                                                  |
|                                                                             |
|o31 = {-3, 2} : 0 <----- 0 : {-1, 1}                                         |
|                     0                                                       |
|                                                                             |
|      {-3, 3} : 0 <----- 0 : {-1, 2}                                         |
|                     0                                                       |
|                                                                             |
|      {-3, 4} : 0 <----- 0 : {-1, 3}                                         |
|                     0                                                       |
|                                                                             |
|      {0, -2} : 0 <----- 0 : {2, -3}                                         |
|                     0                                                       |
|                                                                             |
|      {0, -1} : 0 <----- 0 : {2, -2}                                         |
|                     0                                                       |
|                                                                             |
|                 2               1                                           |
|      {0, 0} : QQ  <---------- QQ  : {2, -1}                                 |
|                      | 1  |                                                 |
|                      | -1 |                                                 |
|                                                                             |
|      {0, 1} : 0 <----- 0 : {2, 0}                                           |
|                    0                                                        |
|                                                                             |
|      {-1, -1} : 0 <----- 0 : {1, -2}                                        |
|                      0                                                      |
|                                                                             |
|      {-1, 0} : 0 <----- 0 : {1, -1}                                         |
|                     0                                                       |
|                                                                             |
|      {-1, 1} : 0 <----- 0 : {1, 0}                                          |
|                     0                                                       |
|                                                                             |
|      {-1, 2} : 0 <----- 0 : {1, 1}                                          |
|                     0                                                       |
|                                                                             |
|      {-2, 0} : 0 <----- 0 : {0, -1}                                         |
|                     0                                                       |
|                                                                             |
|                           2                                                 |
|      {-2, 1} : 0 <----- QQ  : {0, 0}                                        |
|                     0                                                       |
|                                                                             |
|      {-2, 2} : 0 <----- 0 : {0, 1}                                          |
|                     0                                                       |
|                                                                             |
|      {-2, 3} : 0 <----- 0 : {0, 2}                                          |
|                     0                                                       |
|                                                                             |
|      {-3, 1} : 0 <----- 0 : {-1, 0}                                         |
|                     0                                                       |
|                                                                             |
|o31 : SpectralSequencePageMap                                                |
+-----------------------------------------------------------------------------+
|i32 : D^infinity                                                             |
|                                                                             |
|      +------------------------------------------------------------------+   |
|o32 = |subquotient (| 1 0 1  1  0  0  0 0 0 0 |, | 1  1  0  0  0 0 0 0 |)|   |
|      |             | 0 0 -1 0  1  0  0 0 0 0 |  | -1 0  1  0  0 0 0 0 | |   |
|      |             | 0 0 0  -1 -1 1  0 0 0 0 |  | 0  -1 -1 1  0 0 0 0 | |   |
|      |             | 0 1 0  0  0  -1 0 0 0 0 |  | 0  0  0  -1 0 0 0 0 | |   |
|      |                                                                  |   |
|      |{0, 0}                                                            |   |
|      +------------------------------------------------------------------+   |
|                                                                             |
|o32 : Page                                                                   |
+-----------------------------------------------------------------------------+
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:3851:0.

FilteredComplex -- the type of all filtered complexes
*****************************************************

Description
===========

An ascending filtration of a bounded (homological, lower index, or degree $-1$)
chain complex $C : \dots \rightarrow C_i \rightarrow C_{i - 1} \rightarrow
\dots$ is an ordered family of chain subcomplexes $FC : \dots \subseteq F_{n -
1} C \subseteq F_n C \subseteq \dots $. Such a filtration is said to be bounded
if $F_s C = C$ for all sufficiently large $s$ and $F_t C = 0$ for all
sufficiently small $t$.

Alternatively, a descending filtration of a bounded (cohomological, or upper
index, or degree $1$) chain complex $C : \dots  \rightarrow C^i \rightarrow
C^{i + 1} \rightarrow \dots $ is an ordered family of subchain complexes $FC :
\dots \subseteq F^{n + 1} C \subseteq F^n C \subseteq \dots$. Such a filtration
is said to be bounded if $F^s C = 0$ for all sufficiently large $s$ and $F^t C
= C$ for all sufficiently small $t$.

The type FilteredComplex is a data type for working with bounded filtrations of
bounded chain complexes.

Caveat
======

By assumption all filtered complexes arise from bounded filtrations of bounded
chain complexes.  Filtrations on degree $-1$ chain complexes are ascending.
Filtrations on degree $1$ chain complexes are descending.

See also
========

  * How to make filtered complexes from chain complex maps
  * Filtered complexes and simplicial complexes
  * Filtrations and tensor product complexes
  * Filtrations and homomorphism complexes

Functions and methods returning a filtered chain complex:
=========================================================

  * ChainComplex ** FilteredComplex,
    -- filtered tensor product of complexes
  * "FilteredComplex ** ChainComplex" -- see ChainComplex ** FilteredComplex,
    -- filtered tensor
    product of complexes
  * filteredComplex(ChainComplex), --
    obtain a filtered complex from a chain complex
  * filteredComplex(Ideal,ChainComplex,ZZ)
    -- I-adic filtrations of
    chain complexes
  * filteredComplex(List) -- obtain a
    filtered complex from a list of chain complex maps or a nested list of
    simplicial complexes
  * filteredComplex(SpectralSequence)
    -- obtain the filtered complex
    associated to the spectral sequence
  * "Hom(ChainComplex,FilteredComplex)" -- see
    Hom(FilteredComplex,ChainComplex),
    -- the filtered Hom complex
  * Hom(FilteredComplex,ChainComplex)
    -- the filtered Hom complex

Methods that use a filtered chain complex:
==========================================

  * "associatedGradedHomologyObject(ZZ,ZZ,FilteredComplex)" -- see
    associatedGradedHomologyObject, -- compute
    the associated graded homology object
  * chainComplex(FilteredComplex), --
    the ambient chain complex of a filtered complex
  * "FilteredComplex ^ InfiniteNumber" -- see FilteredComplex ^ ZZ,
    -- the filtered pieces
  * FilteredComplex ^ ZZ -- the filtered pieces
  * "FilteredComplex _ InfiniteNumber" -- see FilteredComplex _ ZZ,
    -- the filtered pieces
  * FilteredComplex _ ZZ -- the filtered pieces
  * filteredHomologyObject(ZZ,ZZ,FilteredComplex)
    -- compute the
    filtered homology object
  * inducedMap(FilteredComplex,ZZ),
    -- the i th inclusion map in a filtered complex
  * max(FilteredComplex) -- maximum spot where
    the given filtered complex has a module.
  * min(FilteredComplex) -- minimum spot where
    the given filtered complex has a module.
  * net(FilteredComplex)
  * spectralSequence(FilteredComplex)
    -- construct a spectral sequence
    from a filtered complex
  * spectralSequencePage(FilteredComplex,ZZ)
    -- construct a spectral
    sequence page from a filtered complex
  * "spectralSequencePageMap(FilteredComplex,ZZ)" -- see
    spectralSequencePageMap, -- compute the maps on a
    spectral sequence page
  * spots(FilteredComplex) -- which spots
    does the given filtered complex has a module.
  * support(FilteredComplex)

For the programmer
==================

The object FilteredComplex, is a type (Macaulay2Doc),
with ancestor classes HashTable (Macaulay2Doc),
< Thing (Macaulay2Doc).

-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2141:0.

filteredComplex -- make a filtered complex
******************************************

  * Usage:
        K = filteredComplex L
  * Inputs:
      * L, a list (Macaulay2Doc), or
      * L, a chain complex (OldChainComplexes), or
      * L, a spectral sequence,
  * Optional inputs (Macaulay2Doc),:
      * ReducedHomology,
        => a
        Boolean value (Macaulay2Doc), default value true,
      * Shift, => an
        integer (Macaulay2Doc), default value 0,
  * Outputs:
      * K, a filtered chain complex,

Description
===========

This is the primitive filtered complex constructor.

See also
========

  * FilteredComplex -- the type of all filtered
    complexes
  * How to make filtered complexes from chain complex maps
  * Filtrations and tensor product complexes
  * Filtrations and homomorphism complexes
  * Filtered complexes and simplicial complexes

Ways to use filteredComplex:
============================

  * filteredComplex(ChainComplex), --
    obtain a filtered complex from a chain complex
  * filteredComplex(Ideal,ChainComplex,ZZ)
    -- I-adic filtrations of
    chain complexes
  * filteredComplex(List) -- obtain a
    filtered complex from a list of chain complex maps or a nested list of
    simplicial complexes
  * filteredComplex(SpectralSequence)
    -- obtain the filtered complex
    associated to the spectral sequence

For the programmer
==================

The object filteredComplex, is a method function with options (Macaulay2Doc).

-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2619:0.

FilteredComplex ^ ZZ -- the filtered pieces
*******************************************

  * Operator: ^ (Macaulay2Doc),
  * Usage:
        C = K ^  j
  * Inputs:
      * K, a filtered chain complex,
      * j, an integer (Macaulay2Doc), an integer, infinity, or
        -infinity
  * Outputs:
      * C, a chain complex (OldChainComplexes),

Description
===========

Returns the chain complex in (cohomological) filtration degree j. The
relationship $K ^ j = K _{(-j)}$ holds.

+------------------------------------------------------+
|i1 : A = QQ[x,y];                                     |
+------------------------------------------------------+
|i2 : C = koszul vars A;                               |
+------------------------------------------------------+
|i3 : K = filteredComplex C                            |
|                                                      |
|o3 = -1 : image 0 <-- image 0 <-- image 0             |
|                                                      |
|          0           1           2                   |
|                                                      |
|     0 : image | 1 | <-- image 0 <-- image 0          |
|                                                      |
|         0               1           2                |
|                                                      |
|     1 : image | 1 | <-- image {1} | 1 0 | <-- image 0|
|                               {1} | 0 1 |            |
|         0                                     2      |
|                         1                            |
|                                                      |
|          1      2      1                             |
|     2 : A  <-- A  <-- A                              |
|                                                      |
|         0      1      2                              |
|                                                      |
|o3 : FilteredComplex                                  |
+------------------------------------------------------+
|i4 : K_0                                              |
|                                                      |
|o4 = image | 1 | <-- image 0 <-- image 0              |
|                                                      |
|     0               1           2                    |
|                                                      |
|o4 : ChainComplex                                     |
+------------------------------------------------------+
|i5 : K_1                                              |
|                                                      |
|o5 = image | 1 | <-- image {1} | 1 0 | <-- image 0    |
|                           {1} | 0 1 |                |
|     0                                     2          |
|                     1                                |
|                                                      |
|o5 : ChainComplex                                     |
+------------------------------------------------------+
|i6 : K_2                                              |
|                                                      |
|      1      2      1                                 |
|o6 = A  <-- A  <-- A                                  |
|                                                      |
|     0      1      2                                  |
|                                                      |
|o6 : ChainComplex                                     |
+------------------------------------------------------+
|i7 : K^(-1)                                           |
|                                                      |
|o7 = image | 1 | <-- image {1} | 1 0 | <-- image 0    |
|                           {1} | 0 1 |                |
|     0                                     2          |
|                     1                                |
|                                                      |
|o7 : ChainComplex                                     |
+------------------------------------------------------+
|i8 : K^(-2)                                           |
|                                                      |
|      1      2      1                                 |
|o8 = A  <-- A  <-- A                                  |
|                                                      |
|     0      1      2                                  |
|                                                      |
|o8 : ChainComplex                                     |
+------------------------------------------------------+
|i9 : K_infinity                                       |
|                                                      |
|      1      2      1                                 |
|o9 = A  <-- A  <-- A                                  |
|                                                      |
|     0      1      2                                  |
|                                                      |
|o9 : ChainComplex                                     |
+------------------------------------------------------+
|i10 : K_(-infinity)                                   |
|                                                      |
|o10 = image 0 <-- image 0 <-- image 0                 |
|                                                      |
|      0           1           2                       |
|                                                      |
|o10 : ChainComplex                                    |
+------------------------------------------------------+
|i11 : K^(-infinity)                                   |
|                                                      |
|       1      2      1                                |
|o11 = A  <-- A  <-- A                                 |
|                                                      |
|      0      1      2                                 |
|                                                      |
|o11 : ChainComplex                                    |
+------------------------------------------------------+
|i12 : K^infinity                                      |
|                                                      |
|o12 = image 0 <-- image 0 <-- image 0                 |
|                                                      |
|      0           1           2                       |
|                                                      |
|o12 : ChainComplex                                    |
+------------------------------------------------------+

See also
========

  * FilteredComplex _ ZZ -- the filtered pieces
  * FilteredComplex _ InfiniteNumber -- the
    filtered pieces

Ways to use this method:
========================

  * "FilteredComplex ^ InfiniteNumber"
  * FilteredComplex ^ ZZ -- the filtered pieces
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:3712:0.

FilteredComplex _ ZZ -- the filtered pieces
*******************************************

  * Operator: _ (Macaulay2Doc),
  * Usage:
        C = K _ j
  * Inputs:
      * K, a filtered chain complex,
      * j, an integer (Macaulay2Doc), an integer, infinity, or
        -infinity
  * Outputs:
      * C, a chain complex (OldChainComplexes),

Description
===========

Returns the chain complex in (homological) filtration degree j. The
relationship        $K _ j = K ^{(-j)}$ holds. Example A = QQ[x,y]; C = koszul
vars A; K = filteredComplex C K_0 K_1 K_2 K^(-1) K^(-2) K_infinity
K_(-infinity) K^(- infinity) K^infinity

See also
========

  * FilteredComplex ^ ZZ -- the filtered pieces
  * FilteredComplex ^ InfiniteNumber -- the
    filtered pieces

Ways to use this method:
========================

  * "FilteredComplex _ InfiniteNumber"
  * FilteredComplex _ ZZ -- the filtered pieces
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:3676:0.

filteredComplex(...,ReducedHomology=>...)
*****************************************

Functions with optional argument named ReducedHomology:
=======================================================

  * filteredComplex(...,ReducedHomology=>...)

Further information
===================

  * Default value: true (Macaulay2Doc),
  * Function: filteredComplex, -- make a filtered
    complex
  * Option key: ReducedHomology, -- name for an optional
    argument
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:1086:0.

filteredComplex(...,Shift=>...)
*******************************

Functions with optional argument named Shift:
=============================================

  * filteredComplex(...,Shift=>...)

Further information
===================

  * Default value: 0
  * Function: filteredComplex, -- make a filtered
    complex
  * Option key: Shift, -- name for an optional argument
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:1091:0.

filteredComplex(ChainComplex) -- obtain a filtered complex from a chain complex
*******************************************************************************

  * Function: filteredComplex,
  * Usage:
        K = filteredComplex C
  * Inputs:
      * C, a chain complex (OldChainComplexes),
  * Optional inputs (Macaulay2Doc),:
      * ReducedHomology,
        => a
        Boolean value (Macaulay2Doc), default value true,
      * Shift, => an
        integer (Macaulay2Doc), default value 0,
  * Outputs:
      * K, a filtered chain complex,

Description
===========

Produces the filtered complex obtained by successively truncating the complex.

+------------------------------------------------------+
|i1 : needsPackage "SpectralSequences"                 |
|                                                      |
|o1 = SpectralSequences                                |
|                                                      |
|o1 : Package                                          |
+------------------------------------------------------+
|i2 : A = QQ[x,y]                                      |
|                                                      |
|o2 = A                                                |
|                                                      |
|o2 : PolynomialRing                                   |
+------------------------------------------------------+
|i3 : C = koszul vars A                                |
|                                                      |
|      1      2      1                                 |
|o3 = A  <-- A  <-- A                                  |
|                                                      |
|     0      1      2                                  |
|                                                      |
|o3 : ChainComplex                                     |
+------------------------------------------------------+
|i4 : K = filteredComplex C                            |
|                                                      |
|o4 = -1 : image 0 <-- image 0 <-- image 0             |
|                                                      |
|          0           1           2                   |
|                                                      |
|     0 : image | 1 | <-- image 0 <-- image 0          |
|                                                      |
|         0               1           2                |
|                                                      |
|     1 : image | 1 | <-- image {1} | 1 0 | <-- image 0|
|                               {1} | 0 1 |            |
|         0                                     2      |
|                         1                            |
|                                                      |
|          1      2      1                             |
|     2 : A  <-- A  <-- A                              |
|                                                      |
|         0      1      2                              |
|                                                      |
|o4 : FilteredComplex                                  |
+------------------------------------------------------+

See also
========

  * truncate(ChainComplex,ZZ) (missing documentation)

Ways to use this method:
========================

  * filteredComplex(ChainComplex), --
    obtain a filtered complex from a chain complex
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2953:0.

filteredComplex(Ideal,ChainComplex,ZZ) -- I-adic filtrations of chain complexes
*******************************************************************************

  * Function: filteredComplex,
  * Usage:
        K = filteredComplex(I,C,n)
  * Inputs:
      * I, an ideal (Macaulay2Doc),
      * C, a chain complex (OldChainComplexes),
      * n, an integer (Macaulay2Doc),
  * Optional inputs (Macaulay2Doc),:
      * ReducedHomology,
        => ...,
        default value true,
      * Shift, => ...,
        default value 0,
  * Outputs:
      * K, a filtered chain complex,

Description
===========

By multiplying a chain complex by successive powers of an ideal we obtain a
filtered complex.

+-----------------------------------------------------------------------------+
|i1 : B = QQ[a..d]                                                            |
|                                                                             |
|o1 = B                                                                       |
|                                                                             |
|o1 : PolynomialRing                                                          |
+-----------------------------------------------------------------------------+
|i2 : J = ideal vars B                                                        |
|                                                                             |
|o2 = ideal (a, b, c, d)                                                      |
|                                                                             |
|o2 : Ideal of B                                                              |
+-----------------------------------------------------------------------------+
|i3 : C = complete res monomialCurveIdeal(B,{1,3,4})                          |
|                                                                             |
|      1      4      4      1                                                 |
|o3 = B  <-- B  <-- B  <-- B  <-- 0                                           |
|                                                                             |
|     0      1      2      3      4                                           |
|                                                                             |
|o3 : ChainComplex                                                            |
+-----------------------------------------------------------------------------+
|i4 : K = filteredComplex(J,C,4)                                              |
|                                                                             |
|o4 = -5 : image 0 <-- image 0 <-- image 0 <-- image 0 <-- image 0            |
|                                                                             |
|          0           1           2           3           4                  |
|                                                                             |
|     -4 : image | a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c      |
|                                                                             |
|          0                                                                  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|     -3 : image | a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3 b2c b2d bc2      |
|                                                                             |
|          0                                                                  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|     -2 : image | a2 ab ac ad b2 bc bd c2 cd d2 | <-- image {2} | a2 0       |
|                                                            {3} | 0  a2      |
|          0                                                 {3} | 0  0       |
|                                                            {3} | 0  0       |
|                                                                             |
|                                                      1                      |
|                                                                             |
|     -1 : image | a b c d | <-- image {2} | a 0 0 0 b 0 0 0 c 0 0 0 d 0      |
|                                      {3} | 0 a 0 0 0 b 0 0 0 c 0 0 0 d      |
|          0                           {3} | 0 0 a 0 0 0 b 0 0 0 c 0 0 0      |
|                                      {3} | 0 0 0 a 0 0 0 b 0 0 0 c 0 0      |
|                                                                             |
|                                1                                            |
|                                                                             |
|          1      4      4      1                                             |
|     0 : B  <-- B  <-- B  <-- B  <-- 0                                       |
|                                                                             |
|         0      1      2      3      4                                       |
|                                                                             |
|o4 : FilteredComplex                                                         |
|-----------------------------------------------------------------------------|
|ab2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d     |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|bcd bd2 c3 c2d cd2 d3 | <-- image {2} | a3 0  0  0  a2b 0   0   0   a2c      |
|                                  {3} | 0  a3 0  0  0   a2b 0   0   0        |
|                                  {3} | 0  0  a3 0  0   0   a2b 0   0        |
|                                  {3} | 0  0  0  a3 0   0   0   a2b 0        |
|                                                                             |
|                            1                                                |
|                                                                             |
|0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0       |
|0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd      |
|a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0       |
|0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0       |
|                                                                             |
|                                                                             |
|                                                                             |
|0 0 | <-- image {4} | a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 | <-- image {5} |      |
|0 0 |           {4} | 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 |                      |
|d 0 |           {4} | 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 |     3                |
|0 d |           {4} | 0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d |                      |
|                                                                             |
|          2                                                                  |
|-----------------------------------------------------------------------------|
| bcd2 bd3 c4 c3d c2d2 cd3 d4 | <-- image {2} | a4 0  0  0  a3b 0   0   0     |
|                                         {3} | 0  a4 0  0  0   a3b 0   0     |
|                                         {3} | 0  0  a4 0  0   0   a3b 0     |
|                                         {3} | 0  0  0  a4 0   0   0   a3b   |
|                                                                             |
|                                   1                                         |
|                                                                             |
|0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0    |
|a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0    |
|0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0    |
|0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd  |
|                                                                             |
|                                                                             |
|                                                                             |
|0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  | <-- image {4} | a2 0  0  0  ab   |
|0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |           {4} | 0  a2 0  0  0    |
|bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |           {4} | 0  0  a2 0  0    |
|0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |           {4} | 0  0  0  a2 0    |
|                                                                             |
|                                                2                            |
|                                                                             |
|a b c d | <-- image 0                                                        |
|                                                                             |
|              4                                                              |
|-----------------------------------------------------------------------------|
|a3c 0   0   0   a3d 0   0   0   a2b2 0    0    0    a2bc 0    0    0    a2bd |
|0   a3c 0   0   0   a3d 0   0   0    a2b2 0    0    0    a2bc 0    0    0    |
|0   0   a3c 0   0   0   a3d 0   0    0    a2b2 0    0    0    a2bc 0    0    |
|0   0   0   a3c 0   0   0   a3d 0    0    0    a2b2 0    0    0    a2bc 0    |
|                                                                             |
|                                                                             |
|                                                                             |
| ac2 0   0   0   acd 0   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   |
| 0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   |
| 0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   |
| 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c |
|                                                                             |
|                                                                             |
|                                                                             |
|0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0 |
|ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0 |
|0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2|
|0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0 |
|-----------------------------------------------------------------------------|
|0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0           |
|a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0           |
|0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2        |
|0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0           |
|                                                                             |
|                                                                             |
|                                                                             |
|b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0   c3 0         |
|0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3        |
|0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0  0         |
|0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0  0         |
|                                                                             |
|                                                                             |
|                                                                             |
| 0  cd 0  0  0  d2 0  0  0  | <-- image {5} | a2 ab ac ad b2 bc bd c2        |
| 0  0  cd 0  0  0  d2 0  0  |                                                |
| 0  0  0  cd 0  0  0  d2 0  |     3                                          |
| c2 0  0  0  cd 0  0  0  d2 |                                                |
|-----------------------------------------------------------------------------|
|0    ab3 0   0   0   ab2c 0    0    0    ab2d 0    0    0    abc2 0          |
|0    0   ab3 0   0   0    ab2c 0    0    0    ab2d 0    0    0    abc2       |
|0    0   0   ab3 0   0    0    ab2c 0    0    0    ab2d 0    0    0          |
|a2d2 0   0   0   ab3 0    0    0    ab2c 0    0    0    ab2d 0    0          |
|                                                                             |
|                                                                             |
|                                                                             |
|0  0  c2d 0   0   0   cd2 0   0   0   d3 0  0  0  | <-- image {4} | a3       |
|0  0  0   c2d 0   0   0   cd2 0   0   0  d3 0  0  |           {4} | 0        |
|c3 0  0   0   c2d 0   0   0   cd2 0   0  0  d3 0  |           {4} | 0        |
|0  c3 0   0   0   c2d 0   0   0   cd2 0  0  0  d3 |           {4} | 0        |
|                                                                             |
|                                                        2                    |
|                                                                             |
|cd d2 | <-- image 0                                                          |
|                                                                             |
|            4                                                                |
|-----------------------------------------------------------------------------|
|0    0    abcd 0    0    0    abd2 0    0                                    |
|0    0    0    abcd 0    0    0    abd2 0                                    |
|abc2 0    0    0    abcd 0    0    0    abd2                                 |
|0    abc2 0    0    0    abcd 0    0    0                                    |
|                                                                             |
|                                                                             |
|                                                                             |
|0  0  0  a2b 0   0   0   a2c 0   0   0   a2d                                 |
|a3 0  0  0   a2b 0   0   0   a2c 0   0   0                                   |
|0  a3 0  0   0   a2b 0   0   0   a2c 0   0                                   |
|0  0  a3 0   0   0   a2b 0   0   0   a2c 0                                   |
|-----------------------------------------------------------------------------|
|0    ac3 0   0   0   ac2d 0    0    0    acd2 0    0                         |
|0    0   ac3 0   0   0    ac2d 0    0    0    acd2 0                         |
|0    0   0   ac3 0   0    0    ac2d 0    0    0    acd2                      |
|abd2 0   0   0   ac3 0    0    0    ac2d 0    0    0                         |
|                                                                             |
|                                                                             |
|                                                                             |
|0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0                        |
|a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0                        |
|0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd                      |
|0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0                        |
|-----------------------------------------------------------------------------|
|0    ad3 0   0   0   b4 0  0  0  b3c 0   0   0   b3d 0   0                   |
|0    0   ad3 0   0   0  b4 0  0  0   b3c 0   0   0   b3d 0                   |
|0    0   0   ad3 0   0  0  b4 0  0   0   b3c 0   0   0   b3d                 |
|acd2 0   0   0   ad3 0  0  0  b4 0   0   0   b3c 0   0   0                   |
|                                                                             |
|                                                                             |
|                                                                             |
|0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0   b3 0  0                  |
|0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0  b3 0                  |
|0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0  0  b3                 |
|abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0  0  0                  |
|-----------------------------------------------------------------------------|
|0   b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0                      |
|0   0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0                      |
|0   0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2                   |
|b3d 0    0    0    b2c2 0    0    0    b2cd 0    0    0                      |
|                                                                             |
|                                                                             |
|                                                                             |
|0  b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0                     |
|0  0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd                   |
|0  0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0                     |
|b3 0   0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0                     |
|-----------------------------------------------------------------------------|
|0    bc3 0   0   0   bc2d 0    0    0    bcd2 0    0    0    bd3 0   0   0   |
|0    0   bc3 0   0   0    bc2d 0    0    0    bcd2 0    0    0   bd3 0   0   |
|0    0   0   bc3 0   0    0    bc2d 0    0    0    bcd2 0    0   0   bd3 0   |
|b2d2 0   0   0   bc3 0    0    0    bc2d 0    0    0    bcd2 0   0   0   bd3 |
|                                                                             |
|                                                                             |
|                                                                             |
|0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0   0   d3 0  0  |
|0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0   0   0  d3 0  |
|bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2 0   0  0  d3 |
|0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0   cd2 0  0  0  |
|-----------------------------------------------------------------------------|
|c4 0  0  0  c3d 0   0   0   c2d2 0    0    0    cd3 0   0   0   d4           |
|0  c4 0  0  0   c3d 0   0   0    c2d2 0    0    0   cd3 0   0   0            |
|0  0  c4 0  0   0   c3d 0   0    0    c2d2 0    0   0   cd3 0   0            |
|0  0  0  c4 0   0   0   c3d 0    0    0    c2d2 0   0   0   cd3 0            |
|                                                                             |
|                                                                             |
|                                                                             |
|0  | <-- image {5} | a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3 b2c           |
|0  |                                                                         |
|0  |     3                                                                   |
|d3 |                                                                         |
|-----------------------------------------------------------------------------|
|0  0  0  | <-- image {4} | a4 0  0  0  a3b 0   0   0   a3c 0   0   0   a3d   |
|d4 0  0  |           {4} | 0  a4 0  0  0   a3b 0   0   0   a3c 0   0   0     |
|0  d4 0  |           {4} | 0  0  a4 0  0   0   a3b 0   0   0   a3c 0   0     |
|0  0  d4 |           {4} | 0  0  0  a4 0   0   0   a3b 0   0   0   a3c 0     |
|                                                                             |
|               2                                                             |
|                                                                             |
|b2d bc2 bcd bd2 c3 c2d cd2 d3 | <-- image 0                                  |
|                                                                             |
|                                    4                                        |
|-----------------------------------------------------------------------------|
|0   0   0   a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    a2c2 |
|a3d 0   0   0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    |
|0   a3d 0   0    0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    |
|0   0   a3d 0    0    0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    |
|-----------------------------------------------------------------------------|
|0    0    0    a2cd 0    0    0    a2d2 0    0    0    ab3 0   0   0   ab2c  |
|a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0    0   ab3 0   0   0     |
|0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0   0   ab3 0   0     |
|0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0   0   0   ab3 0     |
|-----------------------------------------------------------------------------|
|0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0      |
|ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0      |
|0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0      |
|0    0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd   |
|-----------------------------------------------------------------------------|
|abd2 0    0    0    ac3 0   0   0   ac2d 0    0    0    acd2 0    0    0     |
|0    abd2 0    0    0   ac3 0   0   0    ac2d 0    0    0    acd2 0    0     |
|0    0    abd2 0    0   0   ac3 0   0    0    ac2d 0    0    0    acd2 0     |
|0    0    0    abd2 0   0   0   ac3 0    0    0    ac2d 0    0    0    acd2  |
|-----------------------------------------------------------------------------|
|ad3 0   0   0   b4 0  0  0  b3c 0   0   0   b3d 0   0   0   b2c2 0    0      |
|0   ad3 0   0   0  b4 0  0  0   b3c 0   0   0   b3d 0   0   0    b2c2 0      |
|0   0   ad3 0   0  0  b4 0  0   0   b3c 0   0   0   b3d 0   0    0    b2c2   |
|0   0   0   ad3 0  0  0  b4 0   0   0   b3c 0   0   0   b3d 0    0    0      |
|-----------------------------------------------------------------------------|
|0    b2cd 0    0    0    b2d2 0    0    0    bc3 0   0   0   bc2d 0    0     |
|0    0    b2cd 0    0    0    b2d2 0    0    0   bc3 0   0   0    bc2d 0     |
|0    0    0    b2cd 0    0    0    b2d2 0    0   0   bc3 0   0    0    bc2d  |
|b2c2 0    0    0    b2cd 0    0    0    b2d2 0   0   0   bc3 0    0    0     |
|-----------------------------------------------------------------------------|
|0    bcd2 0    0    0    bd3 0   0   0   c4 0  0  0  c3d 0   0   0   c2d2    |
|0    0    bcd2 0    0    0   bd3 0   0   0  c4 0  0  0   c3d 0   0   0       |
|0    0    0    bcd2 0    0   0   bd3 0   0  0  c4 0  0   0   c3d 0   0       |
|bc2d 0    0    0    bcd2 0   0   0   bd3 0  0  0  c4 0   0   0   c3d 0       |
|-----------------------------------------------------------------------------|
|0    0    0    cd3 0   0   0   d4 0  0  0  | <-- image {5} | a4 a3b a3c a3d  |
|c2d2 0    0    0   cd3 0   0   0  d4 0  0  |                                 |
|0    c2d2 0    0   0   cd3 0   0  0  d4 0  |     3                           |
|0    0    c2d2 0   0   0   cd3 0  0  0  d4 |                                 |
|-----------------------------------------------------------------------------|
|a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab2d abc2 abcd abd2 ac3 ac2d acd2 ad3 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 bd3 c4 c3d c2d2 cd3 d4 | <-- image 0 |
|                                                                             |
|                                                                     4       |
+-----------------------------------------------------------------------------+

Here are higher some pages of the associated spectral sequence:

+-----------------------------------------------------------------------------+
|i5 : e = prune spectralSequence K                                            |
|                                                                             |
|o5 = e                                                                       |
|                                                                             |
|o5 : SpectralSequence                                                        |
+-----------------------------------------------------------------------------+
|i6 : e^2                                                                     |
|                                                                             |
|     +-----------------------------------------------------------------------|
|o6 = |cokernel {4} | -d -b -d -c 0  0  -d 0  0  0  0  0  -d 0  0  0  0  0  0 |
|     |         {4} | c  a  0  0  0  -d 0  -d -b 0  0  -d 0  0  0  -d 0  0  0 |
|     |         {4} | 0  0  b  a  -d 0  0  0  0  0  -d 0  0  0  0  0  -d -c 0 |
|     |         {4} | 0  0  0  0  c  b  a  0  0  -d 0  0  0  -d 0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  c  a  0  0  0  0  0  -d 0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  b  a  -d|
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |                                                                       |
|     |{-4, 4}                                                                |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 3}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 2}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 1}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 0}                                                                |
|     +-----------------------------------------------------------------------|
|                                                                             |
|o6 : SpectralSequencePage                                                    |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  0|
| -d 0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  -d 0  0  0  0  -d 0  0  0  0|
| 0  0  0  0  0  -d -b 0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  -d 0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  -d 0  0  0  -d 0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  -|
| b  a  -d 0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  -d 0  0  0  0  0  0|
| 0  0  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  -d 0  0  0|
| 0  0  0  0  0  c  a  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  c  b  a  0  0  0  0  0  0  0  0  0  -d 0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  b|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  -d 0  0  0  |
|d -c 0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  |
|  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  -d 0  0  0  0  -d |
|  0  0  0  0  0  0  0  0  0  0  -d -b 0  0  -d 0  0  0  -d 0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  -d 0  |
|  a  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  c  b  a  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  c  b  a  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  c  a  0  0  0  0  0  -d 0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  d  c  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  -d 0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  -d 0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|-d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0  0  0 |
|0  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  -d -c 0  0  -d 0 |
|0  0  0  0  0  -d 0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0 |
|0  0  0  0  0  0  0  0  0  -d 0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0 |
|0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  b  a  -d 0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  -d|
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0  0  0  0  0  0  0  0  c2  -ac 0   0   -cd -ad 0   0   0   -d2 -bd 0   0   |
| 0  0  0  0  0  0  0  0  -bd b2  -d2 0   0   0   0   0   0   0   0   0   0   |
| 0  0  0  0  0  0  0  0  0   0   c2  cd  0   0   0   0   -d2 0   0   0   0   |
| 0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   -d2 0   0   0   0   0   |
| 0  0  0  0  0  0  0  0  0   0   0   -d2 bd  b2  0   0   0   0   0   0   0   |
| 0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   |
| 0  0  0  0  0  0  0  0  0   0   0   0   0   0   -d2 0   0   0   0   0   0   |
| 0  0  0  0  0  0  0  0  0   0   0   0   0   0   cd  c2  0   0   0   -d2 0   |
| 0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   |
| 0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   |
| 0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   d2  bd  b2  0   0   |
| 0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   |
| 0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   d2  0   |
| 0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   |
| 0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   |
| 0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   -d2 |
| 0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   d2  |
| 0  -d 0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   |
| -d 0  0  0  -d 0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   |
| 0  0  0  -d 0  0  0  -d 0   0   0   0   0   0   0   0   0   0   0   0   0   |
| 0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   |
| 0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   |
| 0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   |
| 0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   |
| 0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   |
| 0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   |
| 0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   |
| 0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   |
| 0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   |
| 0  0  0  0  0  0  -d 0  0   0   0   0   0   0   0   0   0   0   0   0   0   |
| 0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   |
| 0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   |
| b  a  -d 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   |
| 0  0  c  b  a  -d 0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   |
| 0  0  0  0  0  c  b  a  0   0   0   0   0   0   0   0   0   0   0   0   0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|---------------------------------------------+-------------------------------|
|0   0   0   0   0   0   0   0   0   0   0   ||0                              |
|0   0   0   -d2 -bd 0   0   0   0   0   0   ||                               |
|0   0   0   0   0   0   0   0   0   0   0   ||{-3, 4}                        |
|0   0   -d2 0   0   0   0   0   0   0   0   ||                               |
|0   0   0   0   0   0   0   0   0   0   0   ||                               |
|0   0   0   0   0   0   0   0   0   0   0   ||                               |
|0   0   0   0   0   0   0   0   0   0   0   ||                               |
|0   0   0   0   0   0   0   0   0   0   0   ||                               |
|0   -d2 0   0   0   -d2 0   0   0   0   0   ||                               |
|-d2 0   0   0   0   0   0   0   0   0   0   ||                               |
|0   0   0   0   0   0   0   0   0   0   0   ||                               |
|0   0   0   0   0   0   0   0   0   0   0   ||                               |
|0   0   0   0   0   0   0   0   0   0   0   ||                               |
|0   0   0   0   0   0   0   0   0   0   0   ||                               |
|0   0   0   0   0   0   0   0   0   0   0   ||                               |
|0   0   0   0   0   0   0   0   0   0   0   ||                               |
|cd  c2  0   0   0   0   0   0   0   0   0   ||                               |
|0   0   0   0   0   0   -d2 0   0   -d2 0   ||                               |
|0   0   0   0   0   0   0   0   -d2 0   0   ||                               |
|0   0   0   0   0   0   0   -d2 0   0   0   ||                               |
|0   0   d2  bd  b2  0   0   0   0   0   0   ||                               |
|0   0   0   0   0   0   0   0   0   0   0   ||                               |
|0   0   0   0   0   d2  0   0   0   0   0   ||                               |
|0   0   0   0   0   0   0   0   0   0   0   ||                               |
|0   0   0   0   0   0   0   0   0   0   0   ||                               |
|0   0   0   0   0   0   d2  0   0   0   0   ||                               |
|0   0   0   0   0   0   0   0   0   0   0   ||                               |
|0   0   0   0   0   0   0   0   0   0   0   ||                               |
|0   0   0   0   0   0   0   0   0   0   0   ||                               |
|0   0   0   0   0   0   0   0   0   0   -d2 ||                               |
|0   0   0   0   0   0   0   d2  cd  c2  0   ||                               |
|0   0   0   0   0   0   0   0   0   0   d2  ||                               |
|0   0   0   0   0   0   0   0   0   0   0   ||                               |
|0   0   0   0   0   0   0   0   0   0   0   ||                               |
|0   0   0   0   0   0   0   0   0   0   0   ||                               |
|                                             |                               |
|                                             |                               |
|---------------------------------------------+-------------------------------|
|                                             |cokernel {3} | d c b a 0 0 0 0 |
|                                             |         {3} | 0 0 0 0 d c b a |
|                                             |         {3} | 0 0 0 0 0 0 0 0 |
|                                             |         {3} | 0 0 0 0 0 0 0 0 |
|                                             |         {3} | 0 0 0 0 0 0 0 0 |
|                                             |         {3} | 0 0 0 0 0 0 0 0 |
|                                             |         {3} | 0 0 0 0 0 0 0 0 |
|                                             |         {3} | 0 0 0 0 0 0 0 0 |
|                                             |         {3} | 0 0 0 0 0 0 0 0 |
|                                             |         {3} | 0 0 0 0 0 0 0 0 |
|                                             |         {3} | 0 0 0 0 0 0 0 0 |
|                                             |         {3} | 0 0 0 0 0 0 0 0 |
|                                             |         {3} | 0 0 0 0 0 0 0 0 |
|                                             |         {3} | 0 0 0 0 0 0 0 0 |
|                                             |         {3} | 0 0 0 0 0 0 0 0 |
|                                             |         {3} | 0 0 0 0 0 0 0 0 |
|                                             |         {3} | 0 0 0 0 0 0 0 0 |
|                                             |         {3} | 0 0 0 0 0 0 0 0 |
|                                             |         {3} | 0 0 0 0 0 0 0 0 |
|                                             |         {3} | 0 0 0 0 0 0 0 0 |
|                                             |                               |
|                                             |{-3, 3}                        |
|                                             |                               |
|                                             |                               |
|                                             |                               |
|                                             |                               |
|                                             |                               |
|---------------------------------------------+-------------------------------|
|                                             |0                              |
|                                             |                               |
|                                             |{-3, 2}                        |
|                                             |                               |
|                                             |                               |
|                                             |                               |
|                                             |                               |
|                                             |                               |
|                                             |                               |
|                                             |                               |
|                                             |                               |
|                                             |                               |
|                                             |                               |
|                                             |                               |
|---------------------------------------------+-------------------------------|
|                                             |0                              |
|                                             |                               |
|                                             |{-3, 1}                        |
|                                             |                               |
|                                             |                               |
|                                             |                               |
|---------------------------------------------+-------------------------------|
|                                             |0                              |
|                                             |                               |
|                                             |{-3, 0}                        |
|---------------------------------------------+-------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|--------------------------------------------------------------------+--------|
|                                                                    |0       |
|                                                                    |        |
|                                                                    |{-2, 4} |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|--------------------------------------------------------------------+--------|
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||cokernel|
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||        |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||        |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||        |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||        |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||        |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||        |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||        |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||        |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||        |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||        |
| a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||        |
| 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||        |
| 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||        |
| 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||        |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||        |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 ||        |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 ||        |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 ||        |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a ||        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |{-2, 3} |
|--------------------------------------------------------------------+--------|
|                                                                    |cokernel|
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|                                                                    |{-2, 2} |
|                                                                    |        |
|                                                                    |        |
|--------------------------------------------------------------------+--------|
|                                                                    |0       |
|                                                                    |        |
|                                                                    |{-2, 1} |
|                                                                    |        |
|                                                                    |        |
|                                                                    |        |
|--------------------------------------------------------------------+--------|
|                                                                    |0       |
|                                                                    |        |
|                                                                    |{-2, 0} |
|--------------------------------------------------------------------+--------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| {4} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| {4} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| {4} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| {4} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 |
| {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 |
| {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 |
| {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b |
| {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| {2} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| {2} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| {2} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| {2} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 |
| {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 |
| {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 |
| {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b |
| {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c|
|a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|a 0 0 0 0 |                                                                  |
|0 d c b a |                                                                  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|------------------------------------------------------+----------------------|
|                                                      |0                     |
|                                                      |                      |
|                                                      |{-1, 4}               |
|                                                      |                      |
|                                                      |                      |
|                                                      |                      |
|                                                      |                      |
|                                                      |                      |
|                                                      |                      |
|                                                      |                      |
|                                                      |                      |
|                                                      |                      |
|                                                      |                      |
|                                                      |                      |
|                                                      |                      |
|                                                      |                      |
|                                                      |                      |
|                                                      |                      |
|                                                      |                      |
|                                                      |                      |
|                                                      |                      |
|                                                      |                      |
|                                                      |                      |
|                                                      |                      |
|                                                      |                      |
|                                                      |                      |
|                                                      |                      |
|                                                      |                      |
|                                                      |                      |
|                                                      |                      |
|                                                      |                      |
|                                                      |                      |
|                                                      |                      |
|                                                      |                      |
|                                                      |                      |
|                                                      |                      |
|                                                      |                      |
|------------------------------------------------------+----------------------|
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||0                     |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                      |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||{-1, 3}               |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                      |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                      |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                      |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                      |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                      |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                      |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                      |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                      |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                      |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                      |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                      |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                      |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                      |
| b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                      |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                      |
| 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                      |
| 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                      |
| 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 ||                      |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                      |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 ||                      |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 ||                      |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a ||                      |
|                                                      |                      |
|                                                      |                      |
|------------------------------------------------------+----------------------|
|                                                      |cokernel {3} | d c b a|
|                                                      |         {4} | 0 0 0 0|
|                                                      |         {3} | 0 0 0 0|
|                                                      |         {4} | 0 0 0 0|
|                                                      |         {3} | 0 0 0 0|
|                                                      |         {4} | 0 0 0 0|
|                                                      |         {4} | 0 0 0 0|
|                                                      |         {4} | 0 0 0 0|
|                                                      |         {3} | 0 0 0 0|
|                                                      |         {4} | 0 0 0 0|
|                                                      |         {4} | 0 0 0 0|
|                                                      |         {4} | 0 0 0 0|
|                                                      |                      |
|                                                      |{-1, 2}               |
|------------------------------------------------------+----------------------|
|                                                      |cokernel {1} | d c b a|
|                                                      |         {1} | 0 0 0 0|
|                                                      |         {1} | 0 0 0 0|
|                                                      |         {1} | 0 0 0 0|
|                                                      |                      |
|                                                      |{-1, 1}               |
|------------------------------------------------------+----------------------|
|                                                      |0                     |
|                                                      |                      |
|                                                      |{-1, 0}               |
|------------------------------------------------------+----------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0 0 0 0 0 0 0 0 0 0 0 0 |                                                   |
| d c b a 0 0 0 0 0 0 0 0 |                                                   |
| 0 0 0 0 d c b a 0 0 0 0 |                                                   |
| 0 0 0 0 0 0 0 0 d c b a |                                                   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-------------+------------------------------------------------+              |
|             |0                                               |              |
|             |                                                |              |
|             |{0, 4}                                          |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|-------------+------------------------------------------------+              |
|             |0                                               |              |
|             |                                                |              |
|             |{0, 3}                                          |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|             |                                                |              |
|-------------+------------------------------------------------+              |
|0 0 0 0 0 0 ||0                                               |              |
|0 0 0 0 0 0 ||                                                |              |
|0 0 0 0 0 0 ||{0, 2}                                          |              |
|0 0 0 0 0 0 ||                                                |              |
|0 0 0 0 0 0 ||                                                |              |
|0 0 0 0 0 0 ||                                                |              |
|0 0 0 0 0 0 ||                                                |              |
|0 0 0 0 0 0 ||                                                |              |
|0 0 0 0 0 0 ||                                                |              |
|0 0 0 0 0 0 ||                                                |              |
|b a 0 0 0 0 ||                                                |              |
|0 0 d c b a ||                                                |              |
|             |                                                |              |
|             |                                                |              |
|-------------+------------------------------------------------+              |
|             |cokernel {2} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 ||              |
|             |         {3} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 ||              |
|             |         {3} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 ||              |
|             |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a ||              |
|             |                                                |              |
|             |{0, 1}                                          |              |
|-------------+------------------------------------------------+              |
|             |cokernel | d c b a |                            |              |
|             |                                                |              |
|             |{0, 0}                                          |              |
|-------------+------------------------------------------------+              |
+-----------------------------------------------------------------------------+
|i7 : assert(all(keys support e^0, j -> isIsomorphism                         |
|-----------------------------------------------------------------------------|
|homologyIsomorphism(e,j#0,j#1,0)))                                           |
+-----------------------------------------------------------------------------+
|i8 : assert(all(keys support e^1, j -> isIsomorphism                         |
|-----------------------------------------------------------------------------|
|homologyIsomorphism(e,j#0,j#1,1)))                                           |
+-----------------------------------------------------------------------------+
|i9 : assert(all(keys support e^2, j -> isIsomorphism                         |
|-----------------------------------------------------------------------------|
|homologyIsomorphism(e,j#0,j#1,2)))                                           |
+-----------------------------------------------------------------------------+
|i10 : assert(all(keys support e^3, j -> isIsomorphism                        |
|-----------------------------------------------------------------------------|
|homologyIsomorphism(e,j#0,j#1,3)))                                           |
+-----------------------------------------------------------------------------+
|i11 : assert(all(keys support e^4, j -> isIsomorphism                        |
|-----------------------------------------------------------------------------|
|homologyIsomorphism(e,j#0,j#1,4)))                                           |
+-----------------------------------------------------------------------------+

Ways to use this method:
========================

  * filteredComplex(Ideal,ChainComplex,ZZ)
    -- I-adic filtrations of
    chain complexes
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:4060:0.

filteredComplex(List) -- obtain a filtered complex from a list of chain complex maps or a nested list of simplicial complexes
*****************************************************************************************************************************

  * Function: filteredComplex,
  * Usage:
        K = filteredComplex L
  * Inputs:
      * L, a list (Macaulay2Doc),
  * Optional inputs (Macaulay2Doc),:
      * ReducedHomology,
        => a
        Boolean value (Macaulay2Doc), default value true,
      * Shift, => an
        integer (Macaulay2Doc), default value 0,
  * Outputs:
      * K, a filtered chain complex,

Description
===========

We can make a filtered complex from a list of chain complex maps as follows. We
first need to load the relevant packages.

+-------------------------------------+
|i1 : needsPackage "SpectralSequences"|
|                                     |
|o1 = SpectralSequences               |
|                                     |
|o1 : Package                         |
+-------------------------------------+

We then make a chain complex.

+------------------------------+
|i2 : R = QQ[x,y,z,w]          |
|                              |
|o2 = R                        |
|                              |
|o2 : PolynomialRing           |
+------------------------------+
|i3 : d2 = matrix(R,{{1},{0}}) |
|                              |
|o3 = | 1 |                    |
|     | 0 |                    |
|                              |
|             2      1         |
|o3 : Matrix R  <-- R          |
+------------------------------+
|i4 : d1 = matrix(R,{{0,1}})   |
|                              |
|o4 = | 0 1 |                  |
|                              |
|             1      2         |
|o4 : Matrix R  <-- R          |
+------------------------------+
|i5 : C = chainComplex({d1,d2})|
|                              |
|      1      2      1         |
|o5 = R  <-- R  <-- R          |
|                              |
|     0      1      2          |
|                              |
|o5 : ChainComplex             |
+------------------------------+

We now make the modules of the another chain complex which we will label D.

+-----------------------------------------------------------------------------+
|i6 : D_2 = image matrix(R,{{1}})                                             |
|                                                                             |
|o6 = image | 1 |                                                             |
|                                                                             |
|                             1                                               |
|o6 : R-module, submodule of R                                                |
+-----------------------------------------------------------------------------+
|i7 : D_1 = image matrix(R,{{1,0},{0,0}})                                     |
|                                                                             |
|o7 = image | 1 0 |                                                           |
|           | 0 0 |                                                           |
|                                                                             |
|                             2                                               |
|o7 : R-module, submodule of R                                                |
+-----------------------------------------------------------------------------+
|i8 : D_0 = image matrix(R,{{1}})                                             |
|                                                                             |
|o8 = image | 1 |                                                             |
|                                                                             |
|                             1                                               |
|o8 : R-module, submodule of R                                                |
+-----------------------------------------------------------------------------+
|i9 : D = chainComplex({inducedMap(D_0,D_1,C.dd_1),inducedMap(D_1,D_2,C.dd_2  |
|                                                                             |
|o9 = image | 1 | <-- image | 1 0 | <-- image | 1 |                           |
|                           | 0 0 |                                           |
|     0                                 2                                     |
|                     1                                                       |
|                                                                             |
|o9 : ChainComplex                                                            |
|-----------------------------------------------------------------------------|
|)})                                                                          |
+-----------------------------------------------------------------------------+

Now make a chain complex map.

+-----------------------------------------------------------------------------+
|i10 : d = chainComplexMap(C,D,apply(spots C, i-> inducedMap(C_i,D_i,id_C     |
|                                                                             |
|           1                                                                 |
|o10 = 0 : R  <--------- image | 1 | : 0                                      |
|                | 1 |                                                        |
|                                                                             |
|           2                                                                 |
|      1 : R  <----------- image | 1 0 | : 1                                  |
|                | 1 0 |         | 0 0 |                                      |
|                | 0 0 |                                                      |
|                                                                             |
|           1                                                                 |
|      2 : R  <--------- image | 1 | : 2                                      |
|                | 1 |                                                        |
|                                                                             |
|o10 : ChainComplexMap                                                        |
|-----------------------------------------------------------------------------|
|_i)))                                                                        |
+-----------------------------------------------------------------------------+
|i11 : isChainComplexMap d                                                    |
|                                                                             |
|o11 = true                                                                   |
+-----------------------------------------------------------------------------+
|i12 : d == chainComplexMap(C,D,{inducedMap(C_0,D_0,id_(C_0)),inducedMap(C_1,D|
|                                                                             |
|o12 = true                                                                   |
|-----------------------------------------------------------------------------|
|_1,id_(C_1)),inducedMap(C_2,D_2,id_(C_2))})                                  |
+-----------------------------------------------------------------------------+

We now make the modules of another chain complex which we will label E.

+-----------------------------------------------------------------------------+
|i13 : E_2 = image matrix(R,{{0}})                                            |
|                                                                             |
|o13 = image 0                                                                |
|                                                                             |
|                              1                                              |
|o13 : R-module, submodule of R                                               |
+-----------------------------------------------------------------------------+
|i14 : E_1 = image matrix(R,{{1,0},{0,0}})                                    |
|                                                                             |
|o14 = image | 1 0 |                                                          |
|            | 0 0 |                                                          |
|                                                                             |
|                              2                                              |
|o14 : R-module, submodule of R                                               |
+-----------------------------------------------------------------------------+
|i15 : E_0 = image matrix(R,{{1}})                                            |
|                                                                             |
|o15 = image | 1 |                                                            |
|                                                                             |
|                              1                                              |
|o15 : R-module, submodule of R                                               |
+-----------------------------------------------------------------------------+
|i16 : E = chainComplex({inducedMap(E_0,E_1,C.dd_1),inducedMap(E_1,E_2,C.dd_2 |
|                                                                             |
|o16 = image | 1 | <-- image | 1 0 | <-- image 0                              |
|                            | 0 0 |                                          |
|      0                                 2                                    |
|                      1                                                      |
|                                                                             |
|o16 : ChainComplex                                                           |
|-----------------------------------------------------------------------------|
|)})                                                                          |
+-----------------------------------------------------------------------------+

Now make a chain complex map.

+-----------------------------------------------------------------------------+
|i17 : e = chainComplexMap(C,E,apply(spots C, i->inducedMap(C_i,D_i, id_C     |
|                                                                             |
|           1                                                                 |
|o17 = 0 : R  <--------- image | 1 | : 0                                      |
|                | 1 |                                                        |
|                                                                             |
|           2                                                                 |
|      1 : R  <----------- image | 1 0 | : 1                                  |
|                | 1 0 |         | 0 0 |                                      |
|                | 0 0 |                                                      |
|                                                                             |
|           1                                                                 |
|      2 : R  <--------- image | 1 | : 2                                      |
|                | 1 |                                                        |
|                                                                             |
|o17 : ChainComplexMap                                                        |
|-----------------------------------------------------------------------------|
|_i)))                                                                        |
+-----------------------------------------------------------------------------+

Now make a filtered complex from a list of chain complex maps.

+-------------------------------------------------------+
|i18 : K = filteredComplex({d,e})                       |
|                                                       |
|o18 = -1 : image 0 <-- image 0 <-- image 0             |
|                                                       |
|           0           1           2                   |
|                                                       |
|      0 : image | 1 | <-- image | 1 0 | <-- image | 1 ||
|                                | 0 0 |                |
|          0                                 2          |
|                          1                            |
|                                                       |
|      1 : image | 1 | <-- image | 1 0 | <-- image | 1 ||
|                                | 0 0 |                |
|          0                                 2          |
|                          1                            |
|                                                       |
|           1      2      1                             |
|      2 : R  <-- R  <-- R                              |
|                                                       |
|          0      1      2                              |
|                                                       |
|o18 : FilteredComplex                                  |
+-------------------------------------------------------+

We can make a filtered complex, with a specified minimum filtration degree from
a list of ChainComplexMaps by using the Shift option.

+--------------------------------------------------------+
|i19 : L = filteredComplex({d,e},Shift => 1)             |
|                                                        |
|o19 = -2 : image 0 <-- image 0 <-- image 0              |
|                                                        |
|           0           1           2                    |
|                                                        |
|      -1 : image | 1 | <-- image | 1 0 | <-- image | 1 ||
|                                 | 0 0 |                |
|           0                                 2          |
|                           1                            |
|                                                        |
|      0 : image | 1 | <-- image | 1 0 | <-- image | 1 | |
|                                | 0 0 |                 |
|          0                                 2           |
|                          1                             |
|                                                        |
|           1      2      1                              |
|      1 : R  <-- R  <-- R                               |
|                                                        |
|          0      1      2                               |
|                                                        |
|o19 : FilteredComplex                                   |
+--------------------------------------------------------+
|i20 : M = filteredComplex({d,e},Shift => -1)            |
|                                                        |
|o20 = 0 : image 0 <-- image 0 <-- image 0               |
|                                                        |
|          0           1           2                     |
|                                                        |
|      1 : image | 1 | <-- image | 1 0 | <-- image | 1 | |
|                                | 0 0 |                 |
|          0                                 2           |
|                          1                             |
|                                                        |
|      2 : image | 1 | <-- image | 1 0 | <-- image | 1 | |
|                                | 0 0 |                 |
|          0                                 2           |
|                          1                             |
|                                                        |
|           1      2      1                              |
|      3 : R  <-- R  <-- R                               |
|                                                        |
|          0      1      2                               |
|                                                        |
|o20 : FilteredComplex                                   |
+--------------------------------------------------------+

We can make a filtered complex from a nested list of simplicial complexes as
follows

+---------------------------------------------------------------------+
|i21 : D = simplicialComplex {x*y*z, x*y, y*z, w*z}                   |
|                                                                     |
|o21 = simplicialComplex | zw xyz |                                   |
|                                                                     |
|o21 : SimplicialComplex                                              |
+---------------------------------------------------------------------+
|i22 : E = simplicialComplex {x*y, w}                                 |
|                                                                     |
|o22 = simplicialComplex | w xy |                                     |
|                                                                     |
|o22 : SimplicialComplex                                              |
+---------------------------------------------------------------------+
|i23 : F = simplicialComplex {x,w}                                    |
|                                                                     |
|o23 = simplicialComplex | w x |                                      |
|                                                                     |
|o23 : SimplicialComplex                                              |
+---------------------------------------------------------------------+
|i24 : K = filteredComplex{D,E,F}                                     |
|                                                                     |
|o24 = -1 : image 0 <-- image 0 <-- image 0 <-- image 0               |
|                                                                     |
|           -1          0           1           2                     |
|                                                                     |
|      0 : image | 1 | <-- image | 1 0 | <-- image 0 <-- image 0      |
|                                | 0 0 |                              |
|          -1                    | 0 0 |     1           2            |
|                                | 0 1 |                              |
|                                                                     |
|                          0                                          |
|                                                                     |
|      1 : image | 1 | <-- image | 1 0 0 | <-- image | 1 | <-- image 0|
|                                | 0 1 0 |           | 0 |            |
|          -1                    | 0 0 0 |           | 0 |     2      |
|                                | 0 0 1 |           | 0 |            |
|                                                                     |
|                          0                   1                      |
|                                                                     |
|            1       4       4       1                                |
|      2 : QQ  <-- QQ  <-- QQ  <-- QQ                                 |
|                                                                     |
|          -1      0       1       2                                  |
|                                                                     |
|o24 : FilteredComplex                                                |
+---------------------------------------------------------------------+

If we want the resulting complexes to correspond to the non-reduced homology of
the simplicial complexes we can do the following.

+-----------------------------------------------------------------+
|i25 : filteredComplex({D,E,F}, ReducedHomology => false)         |
|                                                                 |
|o25 = -1 : image 0 <-- image 0 <-- image 0 <-- image 0           |
|                                                                 |
|           -1          0           1           2                 |
|                                                                 |
|      0 : image 0 <-- image | 1 0 | <-- image 0 <-- image 0      |
|                            | 0 0 |                              |
|          -1                | 0 0 |     1           2            |
|                            | 0 1 |                              |
|                                                                 |
|                      0                                          |
|                                                                 |
|      1 : image 0 <-- image | 1 0 0 | <-- image | 1 | <-- image 0|
|                            | 0 1 0 |           | 0 |            |
|          -1                | 0 0 0 |           | 0 |     2      |
|                            | 0 0 1 |           | 0 |            |
|                                                                 |
|                      0                   1                      |
|                                                                 |
|                        4       4       1                        |
|      2 : image 0 <-- QQ  <-- QQ  <-- QQ                         |
|                                                                 |
|          -1          0       1       2                          |
|                                                                 |
|o25 : FilteredComplex                                            |
+-----------------------------------------------------------------+

See also
========

  * maps between chain complexes (missing documentation)

Ways to use this method:
========================

  * filteredComplex(List) -- obtain a
    filtered complex from a list of chain complex maps or a nested list of
    simplicial complexes
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2927:0.

filteredComplex(SpectralSequence) -- obtain the filtered complex associated to the spectral sequence
****************************************************************************************************

  * Function: filteredComplex,
  * Usage:
        K = filteredComplex E
  * Inputs:
      * E, a spectral sequence,
  * Optional inputs (Macaulay2Doc),:
      * ReducedHomology,
        => a
        Boolean value (Macaulay2Doc), default value true,
      * Shift, => an
        integer (Macaulay2Doc), default value 0,
  * Outputs:
      * K, a filtered chain complex,

Description
===========

Produces the filtered complex which determined the spectral sequence. Consider
the spectral sequence $E$ which arises from a nested list of simplicial
complexes.

+--------------------------------------------------+
|i1 : A = QQ[a,b,c,d];                             |
+--------------------------------------------------+
|i2 : D = simplicialComplex {a*d*c, a*b, a*c, b*c};|
+--------------------------------------------------+
|i3 : F2D = D;                                     |
+--------------------------------------------------+
|i4 : F1D = simplicialComplex {a*c, d};            |
+--------------------------------------------------+
|i5 : F0D = simplicialComplex {a,d};               |
+--------------------------------------------------+
|i6 : K = filteredComplex {F2D, F1D, F0D};         |
+--------------------------------------------------+
|i7 : E = spectralSequence(K) ;                    |
+--------------------------------------------------+

The underlying filtered chain complex can be recovered from the spectral
sequence by:

+--------------------------------------------------------------------+
|i8 : C = filteredComplex E                                          |
|                                                                    |
|o8 = -1 : image 0 <-- image 0 <-- image 0 <-- image 0               |
|                                                                    |
|          -1          0           1           2                     |
|                                                                    |
|     0 : image | 1 | <-- image | 1 0 | <-- image 0 <-- image 0      |
|                               | 0 0 |                              |
|         -1                    | 0 0 |     1           2            |
|                               | 0 1 |                              |
|                                                                    |
|                         0                                          |
|                                                                    |
|     1 : image | 1 | <-- image | 1 0 0 | <-- image | 0 | <-- image 0|
|                               | 0 0 0 |           | 1 |            |
|         -1                    | 0 1 0 |           | 0 |     2      |
|                               | 0 0 1 |           | 0 |            |
|                                                   | 0 |            |
|                         0                                          |
|                                             1                      |
|                                                                    |
|           1       4       5       1                                |
|     2 : QQ  <-- QQ  <-- QQ  <-- QQ                                 |
|                                                                    |
|         -1      0       1       2                                  |
|                                                                    |
|o8 : FilteredComplex                                                |
+--------------------------------------------------------------------+

Ways to use this method:
========================

  * filteredComplex(SpectralSequence)
    -- obtain the filtered complex
    associated to the spectral sequence
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2991:0.

filteredHomologyObject -- compute the filtered homology object
**************************************************************

See also
========

  * filteredHomologyObject(ZZ,ZZ,FilteredComplex)
    -- compute the
    filtered homology object
  * associatedGradedHomologyObject(ZZ,ZZ,FilteredComplex)
    -- compute the associated graded homology
    object

Ways to use filteredHomologyObject:
===================================

  * filteredHomologyObject(ZZ,ZZ,FilteredComplex)
    -- compute the
    filtered homology object

For the programmer
==================

The object filteredHomologyObject, is a
method function (Macaulay2Doc).

-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:3861:0.

filteredHomologyObject(ZZ,ZZ,FilteredComplex) -- compute the filtered homology object
*************************************************************************************

  * Function: filteredHomologyObject,
  * Usage:
        M = filteredHomologyObject(ZZ, ZZ, FilteredComplex)
  * Inputs:
      * p, an integer (Macaulay2Doc),
      * n, an integer (Macaulay2Doc),
      * K, a filtered chain complex,
  * Outputs:
      * M, a module (Macaulay2Doc),

Description
===========

Computes the filtered homology object determined by the filtered chain complex

See also
========

  * associatedGradedHomologyObject(ZZ,ZZ,FilteredComplex)
    -- compute the associated graded homology
    object

Ways to use this method:
========================

  * filteredHomologyObject(ZZ,ZZ,FilteredComplex)
    -- compute the
    filtered homology object
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:3882:0.

Filtrations and homomorphism complexes
**************************************

Let $S$ be a commutative ring and let $B : \dots \rightarrow B_{i} \rightarrow
B_{i - 1} \rightarrow \cdots $ and $C : \dots \rightarrow C_{i} \rightarrow
C_{i - 1} \rightarrow \cdots $ be chain complexes.

For all integers $p$ and $q$ let $K_{p,q} := Hom_S(B_{-p}, C_q)$, let $d'_{p,q}
: K_{p,q} \rightarrow K_{p - 1, q}$ denote the homorphism $ \phi \mapsto
\partial^B_{-p + 1}  \phi$, and let $d^{''}_{p,q} : K_{p,q} \rightarrow K_{p, q
- 1} $ denote the homorphism $\phi \mapsto (-1)^p \partial^C_q  \phi$.

The chain complex $Hom(B, C)$ is given by $ Hom(B, C)_k := \prod_{p + q = k}
Hom_S(B_{-p}, C_q) $ and the differentials by $ \partial := d^{'} + d^{''} $;
it carries two natural ascending filtrations $F' ( Hom(B, C) )$ and $F''(
Hom(B, C))$.

The first is obtained by letting $F'_n (Hom(B, C))$ be the chain complex
determined by setting $F'_n (Hom(B, C))_k := \prod_{p + q = k , p \leq n}
Hom_S(B_{-p}, C_q)$ and the differentials $\partial := d' + d''$.

The second is obtained by letting $F''_n (Hom(B, C)) := \prod_{p + q = k , q
\leq n} Hom_S(B_{-p}, C_q)$ and the differentials $\partial := d' + d''$.

In Macaulay2, using this package, $F'$ and $F''$ as defined above are computed
as illustrated in the following example, by using Hom(filteredComplex B, C) or
Hom(B,filteredComplex C).

+-----------------------------------------------------------------------------+
|i1 : A = QQ[x,y,z,w];                                                        |
+-----------------------------------------------------------------------------+
|i2 : B = res monomialCurveIdeal(A, {1,2,3});                                 |
+-----------------------------------------------------------------------------+
|i3 : C = res monomialCurveIdeal(A, {1,3,4});                                 |
+-----------------------------------------------------------------------------+
|i4 : F' = Hom(filteredComplex B, C)                                          |
|                                                                             |
|o4 = -3 : image 0 <-- image 0 <-- image 0 <-- image 0 <-- image 0 <-- image 0|
|                                                                             |
|          -3          -2          -1          0           1           2      |
|                                                                             |
|     -2 : image 0 <-- image {-3} | 1 0 | <-- image {-2} | 0 0 0 0 0 0 0 0 0 0|
|                            {-3} | 0 1 |           {-2} | 0 0 0 0 0 0 0 0 0 0|
|          -3                                       {-2} | 0 0 0 0 0 0 0 0 0 0|
|                      -2                           {-1} | 0 0 0 1 0 0 0 0 0 0|
|                                                   {0}  | 0 0 0 0 1 0 0 0 0 0|
|                                                   {0}  | 0 0 0 0 0 1 0 0 0 0|
|                                                   {0}  | 0 0 0 0 0 0 1 0 0 0|
|                                                   {-1} | 0 0 0 0 0 0 0 1 0 0|
|                                                   {0}  | 0 0 0 0 0 0 0 0 1 0|
|                                                   {0}  | 0 0 0 0 0 0 0 0 0 1|
|                                                   {0}  | 0 0 0 0 0 0 0 0 0 0|
|                                                                             |
|                                             -1                              |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|     -1 : image 0 <-- image {-3} | 1 0 | <-- image {-2} | 1 0 0 0 0 0 0 0 0 0|
|                            {-3} | 0 1 |           {-2} | 0 1 0 0 0 0 0 0 0 0|
|          -3                                       {-2} | 0 0 1 0 0 0 0 0 0 0|
|                      -2                           {-1} | 0 0 0 1 0 0 0 0 0 0|
|                                                   {0}  | 0 0 0 0 1 0 0 0 0 0|
|                                                   {0}  | 0 0 0 0 0 1 0 0 0 0|
|                                                   {0}  | 0 0 0 0 0 0 1 0 0 0|
|                                                   {-1} | 0 0 0 0 0 0 0 1 0 0|
|                                                   {0}  | 0 0 0 0 0 0 0 0 1 0|
|                                                   {0}  | 0 0 0 0 0 0 0 0 0 1|
|                                                   {0}  | 0 0 0 0 0 0 0 0 0 0|
|                                                                             |
|                                             -1                              |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                 2      11      21      18      7      1                     |
|     0 : 0  <-- A  <-- A   <-- A   <-- A   <-- A  <-- A  <-- 0               |
|                                                                             |
|         -3     -2     -1      0       1       2      3      4               |
|                                                                             |
|o4 : FilteredComplex                                                         |
|-----------------------------------------------------------------------------|
|<-- image 0 <-- image 0                                                      |
|                                                                             |
|    3           4                                                            |
|                                                                             |
|0 | <-- image {0} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | <-- image {2}|
|0 |           {0} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {3}|
|0 |           {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {3}|
|0 |           {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {3}|
|0 |           {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {2}|
|0 |           {0} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {2}|
|0 |           {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {2}|
|0 |           {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {2}|
|0 |           {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {2}|
|0 |           {0} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {2}|
|1 |           {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {2}|
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {2}|
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {2}|
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 |           {2}|
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 |           {2}|
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 |           {2}|
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 |           {2}|
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 |           {2}|
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 |     1        |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 |              |
|                                                                             |
|        0                                                                    |
|                                                                             |
|0 | <-- image {0} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | <-- image {2}|
|0 |           {0} | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {3}|
|0 |           {1} | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {3}|
|0 |           {1} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {3}|
|0 |           {1} | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {2}|
|0 |           {0} | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {2}|
|0 |           {1} | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {2}|
|0 |           {1} | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {2}|
|0 |           {1} | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |           {2}|
|0 |           {0} | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |           {2}|
|1 |           {1} | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 |           {2}|
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 |           {2}|
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 |           {2}|
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 |           {2}|
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 |           {2}|
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 |           {2}|
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 |           {2}|
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 |           {2}|
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 |     1        |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 |              |
|                                                                             |
|        0                                                                    |
|-----------------------------------------------------------------------------|
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | <-- image 0 <-- image 0 <-- image 0  |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |     2           3           4        |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 |                                      |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | <-- image {4} | 0 0 0 0 0 0 0 | <--  |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {4} | 0 0 0 0 0 0 0 |      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {4} | 0 0 0 0 0 0 0 |      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {4} | 0 0 0 0 0 0 0 |      |
|| 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {3} | 0 0 0 0 1 0 0 |      |
|| 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |           {3} | 0 0 0 0 0 1 0 |      |
|| 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |           {3} | 0 0 0 0 0 0 1 |      |
|| 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 |     2                                |
|| 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 |                                      |
|-----------------------------------------------------------------------------|
|image 0 <-- image 0                                                          |
|                                                                             |
|3           4                                                                |
+-----------------------------------------------------------------------------+
|i5 : F'' = Hom(B,filteredComplex C)                                          |
|                                                                             |
|o5 = -1 : image 0 <-- image 0 <-- image 0 <-- image 0 <-- image 0 <-- image 0|
|                                                                             |
|          -3          -2          -1          0           1           2      |
|                                                                             |
|     0 : image 0 <-- image {-3} | 1 0 | <-- image {-2} | 1 0 0 0 0 0 0 0 0 0 |
|                           {-3} | 0 1 |           {-2} | 0 1 0 0 0 0 0 0 0 0 |
|         -3                                       {-2} | 0 0 1 0 0 0 0 0 0 0 |
|                     -2                           {-1} | 0 0 0 0 0 0 0 0 0 0 |
|                                                  {0}  | 0 0 0 0 0 0 0 0 0 0 |
|                                                  {0}  | 0 0 0 0 0 0 0 0 0 0 |
|                                                  {0}  | 0 0 0 0 0 0 0 0 0 0 |
|                                                  {-1} | 0 0 0 0 0 0 0 0 0 0 |
|                                                  {0}  | 0 0 0 0 0 0 0 0 0 0 |
|                                                  {0}  | 0 0 0 0 0 0 0 0 0 0 |
|                                                  {0}  | 0 0 0 0 0 0 0 0 0 0 |
|                                                                             |
|                                            -1                               |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|     1 : image 0 <-- image {-3} | 1 0 | <-- image {-2} | 1 0 0 0 0 0 0 0 0 0 |
|                           {-3} | 0 1 |           {-2} | 0 1 0 0 0 0 0 0 0 0 |
|         -3                                       {-2} | 0 0 1 0 0 0 0 0 0 0 |
|                     -2                           {-1} | 0 0 0 1 0 0 0 0 0 0 |
|                                                  {0}  | 0 0 0 0 1 0 0 0 0 0 |
|                                                  {0}  | 0 0 0 0 0 1 0 0 0 0 |
|                                                  {0}  | 0 0 0 0 0 0 1 0 0 0 |
|                                                  {-1} | 0 0 0 0 0 0 0 1 0 0 |
|                                                  {0}  | 0 0 0 0 0 0 0 0 1 0 |
|                                                  {0}  | 0 0 0 0 0 0 0 0 0 1 |
|                                                  {0}  | 0 0 0 0 0 0 0 0 0 0 |
|                                                                             |
|                                            -1                               |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|     2 : image 0 <-- image {-3} | 1 0 | <-- image {-2} | 1 0 0 0 0 0 0 0 0 0 |
|                           {-3} | 0 1 |           {-2} | 0 1 0 0 0 0 0 0 0 0 |
|         -3                                       {-2} | 0 0 1 0 0 0 0 0 0 0 |
|                     -2                           {-1} | 0 0 0 1 0 0 0 0 0 0 |
|                                                  {0}  | 0 0 0 0 1 0 0 0 0 0 |
|                                                  {0}  | 0 0 0 0 0 1 0 0 0 0 |
|                                                  {0}  | 0 0 0 0 0 0 1 0 0 0 |
|                                                  {-1} | 0 0 0 0 0 0 0 1 0 0 |
|                                                  {0}  | 0 0 0 0 0 0 0 0 1 0 |
|                                                  {0}  | 0 0 0 0 0 0 0 0 0 1 |
|                                                  {0}  | 0 0 0 0 0 0 0 0 0 0 |
|                                                                             |
|                                            -1                               |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                 2      11      21      18      7      1                     |
|     3 : 0  <-- A  <-- A   <-- A   <-- A   <-- A  <-- A  <-- 0               |
|                                                                             |
|         -3     -2     -1      0       1       2      3      4               |
|                                                                             |
|o5 : FilteredComplex                                                         |
|-----------------------------------------------------------------------------|
| <-- image 0 <-- image 0                                                     |
|                                                                             |
|     3           4                                                           |
|                                                                             |
|0 | <-- image {0} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | <-- image    |
|0 |           {0} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |     1        |
|0 |           {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {0} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {0} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|                                                                             |
|        0                                                                    |
|                                                                             |
|0 | <-- image {0} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | <-- image    |
|0 |           {0} | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {1} | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {1} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {1} | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {0} | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {1} | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {1} | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {1} | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {0} | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |              |
|1 |           {1} | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |     1        |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|                                                                             |
|        0                                                                    |
|                                                                             |
|0 | <-- image {0} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | <-- image    |
|0 |           {0} | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {1} | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {1} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {1} | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {0} | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {1} | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {1} | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {1} | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {0} | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |              |
|1 |           {1} | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 |     1        |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 |              |
|                                                                             |
|        0                                                                    |
|-----------------------------------------------------------------------------|
|0 <-- image 0 <-- image 0 <-- image 0                                        |
|                                                                             |
|      2           3           4                                              |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|{2} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | <-- image 0 <-- image 0 <--      |
|{3} | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                  |
|{3} | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |     2           3                |
|{3} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|{2} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | <-- image {4} | 1 0 0 0 0 0      |
|{3} | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {4} | 0 1 0 0 0 0      |
|{3} | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {4} | 0 0 1 0 0 0      |
|{3} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {4} | 0 0 0 1 0 0      |
|{2} | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {3} | 0 0 0 0 0 0      |
|{2} | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |           {3} | 0 0 0 0 0 0      |
|{2} | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |           {3} | 0 0 0 0 0 0      |
|{2} | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 |     2                            |
|{2} | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                  |
|-----------------------------------------------------------------------------|
|image 0                                                                      |
|                                                                             |
|4                                                                            |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0 | <-- image 0 <-- image 0                                                  |
|0 |                                                                          |
|0 |     3           4                                                        |
|0 |                                                                          |
|0 |                                                                          |
|0 |                                                                          |
|0 |                                                                          |
+-----------------------------------------------------------------------------+

Notice that the display above shows that these are different filtered
complexes. The resulting spectral sequences take the form:

+-----------------------------------------------------------------------------+
|i6 : E' = prune spectralSequence F';                                         |
+-----------------------------------------------------------------------------+
|i7 : E'' = prune spectralSequence F'' ;                                      |
+-----------------------------------------------------------------------------+
|i8 : E' ^0                                                                   |
|                                                                             |
|     +-------+-------+------+                                                |
|     | 2     | 3     | 1    |                                                |
|o8 = |A      |A      |A     |                                                |
|     |       |       |      |                                                |
|     |{-2, 3}|{-1, 3}|{0, 3}|                                                |
|     +-------+-------+------+                                                |
|     | 8     | 12    | 4    |                                                |
|     |A      |A      |A     |                                                |
|     |       |       |      |                                                |
|     |{-2, 2}|{-1, 2}|{0, 2}|                                                |
|     +-------+-------+------+                                                |
|     | 8     | 12    | 4    |                                                |
|     |A      |A      |A     |                                                |
|     |       |       |      |                                                |
|     |{-2, 1}|{-1, 1}|{0, 1}|                                                |
|     +-------+-------+------+                                                |
|     | 2     | 3     | 1    |                                                |
|     |A      |A      |A     |                                                |
|     |       |       |      |                                                |
|     |{-2, 0}|{-1, 0}|{0, 0}|                                                |
|     +-------+-------+------+                                                |
|                                                                             |
|o8 : SpectralSequencePage                                                    |
+-----------------------------------------------------------------------------+
|i9 : E' ^ 0 .dd                                                              |
|                                                                             |
|o9 = {0, -4} : 0 <----- 0 : {0, -3}                                          |
|                    0                                                        |
|                                                                             |
|     {0, -3} : 0 <----- 0 : {0, -2}                                          |
|                    0                                                        |
|                                                                             |
|     {0, -2} : 0 <----- 0 : {0, -1}                                          |
|                    0                                                        |
|                                                                             |
|                         1                                                   |
|     {0, -1} : 0 <----- A  : {0, 0}                                          |
|                    0                                                        |
|                                                                             |
|               1                                       4                     |
|     {0, 0} : A  <----------------------------------- A  : {0, 1}            |
|                    | yz-xw y3-x2z xz2-y2w z3-yw2 |                          |
|                                                                             |
|               4                               4                             |
|     {0, 1} : A  <--------------------------- A  : {0, 2}                    |
|                    {2} | -y2 -xz -yw -z2 |                                  |
|                    {3} | z   w   0   0   |                                  |
|                    {3} | x   y   -z  -w  |                                  |
|                    {3} | 0   0   x   y   |                                  |
|                                                                             |
|               4                  1                                          |
|     {0, 2} : A  <-------------- A  : {0, 3}                                 |
|                    {4} | w  |                                               |
|                    {4} | -z |                                               |
|                    {4} | -y |                                               |
|                    {4} | x  |                                               |
|                                                                             |
|               1                                                             |
|     {0, 3} : A  <----- 0 : {0, 4}                                           |
|                    0                                                        |
|                                                                             |
|     {-1, -3} : 0 <----- 0 : {-1, -2}                                        |
|                     0                                                       |
|                                                                             |
|     {-1, -2} : 0 <----- 0 : {-1, -1}                                        |
|                     0                                                       |
|                                                                             |
|                          3                                                  |
|     {-1, -1} : 0 <----- A  : {-1, 0}                                        |
|                     0                                                       |
|                                                                             |
|                3                                                            |
|     {-1, 0} : A  <----------------------------------------------------------|
|                     {-2} | -yz+xw -y3+x2z -xz2+y2w -z3+yw2 0      0       0 |
|                     {-2} | 0      0       0        0       -yz+xw -y3+x2z -x|
|                     {-2} | 0      0       0        0       0      0       0 |
|                                                                             |
|                12                                                   12      |
|     {-1, 1} : A   <----------------------------------------------- A   : {-1|
|                      {0} | y2 xz yw z2 0  0  0  0  0  0  0  0  |            |
|                      {1} | -z -w 0  0  0  0  0  0  0  0  0  0  |            |
|                      {1} | -x -y z  w  0  0  0  0  0  0  0  0  |            |
|                      {1} | 0  0  -x -y 0  0  0  0  0  0  0  0  |            |
|                      {0} | 0  0  0  0  y2 xz yw z2 0  0  0  0  |            |
|                      {1} | 0  0  0  0  -z -w 0  0  0  0  0  0  |            |
|                      {1} | 0  0  0  0  -x -y z  w  0  0  0  0  |            |
|                      {1} | 0  0  0  0  0  0  -x -y 0  0  0  0  |            |
|                      {0} | 0  0  0  0  0  0  0  0  y2 xz yw z2 |            |
|                      {1} | 0  0  0  0  0  0  0  0  -z -w 0  0  |            |
|                      {1} | 0  0  0  0  0  0  0  0  -x -y z  w  |            |
|                      {1} | 0  0  0  0  0  0  0  0  0  0  -x -y |            |
|                                                                             |
|                12                        3                                  |
|     {-1, 2} : A   <-------------------- A  : {-1, 3}                        |
|                      {2} | -w 0  0  |                                       |
|                      {2} | z  0  0  |                                       |
|                      {2} | y  0  0  |                                       |
|                      {2} | -x 0  0  |                                       |
|                      {2} | 0  -w 0  |                                       |
|                      {2} | 0  z  0  |                                       |
|                      {2} | 0  y  0  |                                       |
|                      {2} | 0  -x 0  |                                       |
|                      {2} | 0  0  -w |                                       |
|                      {2} | 0  0  z  |                                       |
|                      {2} | 0  0  y  |                                       |
|                      {2} | 0  0  -x |                                       |
|                                                                             |
|                3                                                            |
|     {-1, 3} : A  <----- 0 : {-1, 4}                                         |
|                     0                                                       |
|                                                                             |
|     {-1, 4} : 0 <----- 0 : {-1, 5}                                          |
|                    0                                                        |
|                                                                             |
|     {-2, -2} : 0 <----- 0 : {-2, -1}                                        |
|                     0                                                       |
|                                                                             |
|                          2                                                  |
|     {-2, -1} : 0 <----- A  : {-2, 0}                                        |
|                     0                                                       |
|                                                                             |
|                2                                                            |
|     {-2, 0} : A  <----------------------------------------------------------|
|                     {-3} | yz-xw y3-x2z xz2-y2w z3-yw2 0     0      0       |
|                     {-3} | 0     0      0       0      yz-xw y3-x2z xz2-y2w |
|                                                                             |
|                8                                                8           |
|     {-2, 1} : A  <-------------------------------------------- A  : {-2, 2} |
|                     {-1} | -y2 -xz -yw -z2 0   0   0   0   |                |
|                     {0}  | z   w   0   0   0   0   0   0   |                |
|                     {0}  | x   y   -z  -w  0   0   0   0   |                |
|                     {0}  | 0   0   x   y   0   0   0   0   |                |
|                     {-1} | 0   0   0   0   -y2 -xz -yw -z2 |                |
|                     {0}  | 0   0   0   0   z   w   0   0   |                |
|                     {0}  | 0   0   0   0   x   y   -z  -w  |                |
|                     {0}  | 0   0   0   0   0   0   x   y   |                |
|                                                                             |
|                8                     2                                      |
|     {-2, 2} : A  <----------------- A  : {-2, 3}                            |
|                     {1} | w  0  |                                           |
|                     {1} | -z 0  |                                           |
|                     {1} | -y 0  |                                           |
|                     {1} | x  0  |                                           |
|                     {1} | 0  w  |                                           |
|                     {1} | 0  -z |                                           |
|                     {1} | 0  -y |                                           |
|                     {1} | 0  x  |                                           |
|                                                                             |
|                2                                                            |
|     {-2, 3} : A  <----- 0 : {-2, 4}                                         |
|                     0                                                       |
|                                                                             |
|     {-2, 4} : 0 <----- 0 : {-2, 5}                                          |
|                    0                                                        |
|                                                                             |
|     {-2, 5} : 0 <----- 0 : {-2, 6}                                          |
|                    0                                                        |
|                                                                             |
|     {-3, -1} : 0 <----- 0 : {-3, 0}                                         |
|                     0                                                       |
|                                                                             |
|     {-3, 0} : 0 <----- 0 : {-3, 1}                                          |
|                    0                                                        |
|                                                                             |
|     {-3, 1} : 0 <----- 0 : {-3, 2}                                          |
|                    0                                                        |
|                                                                             |
|     {-3, 2} : 0 <----- 0 : {-3, 3}                                          |
|                    0                                                        |
|                                                                             |
|     {-3, 3} : 0 <----- 0 : {-3, 4}                                          |
|                    0                                                        |
|                                                                             |
|     {-3, 4} : 0 <----- 0 : {-3, 5}                                          |
|                    0                                                        |
|                                                                             |
|     {-3, 5} : 0 <----- 0 : {-3, 6}                                          |
|                    0                                                        |
|                                                                             |
|     {-3, 6} : 0 <----- 0 : {-3, 7}                                          |
|                    0                                                        |
|                                                                             |
|o9 : SpectralSequencePageMap                                                 |
|-----------------------------------------------------------------------------|
|                                                    12                       |
|-------------------------------------------------- A   : {-1, 1}             |
|       0       0      0       0        0       |                             |
|z2+y2w -z3+yw2 0      0       0        0       |                             |
|       0       -yz+xw -y3+x2z -xz2+y2w -z3+yw2 |                             |
|                                                                             |
|                                                                             |
|, 2}                                                                         |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|            8                                                                |
|---------- A  : {-2, 1}                                                      |
|0      |                                                                     |
|z3-yw2 |                                                                     |
+-----------------------------------------------------------------------------+
|i10 : E'' ^0                                                                 |
|                                                                             |
|      +-------+-------+-------+-------+                                      |
|      | 1     | 4     | 4     | 1     |                                      |
|o10 = |A      |A      |A      |A      |                                      |
|      |       |       |       |       |                                      |
|      |{0, 0} |{1, 0} |{2, 0} |{3, 0} |                                      |
|      +-------+-------+-------+-------+                                      |
|      | 3     | 12    | 12    | 3     |                                      |
|      |A      |A      |A      |A      |                                      |
|      |       |       |       |       |                                      |
|      |{0, -1}|{1, -1}|{2, -1}|{3, -1}|                                      |
|      +-------+-------+-------+-------+                                      |
|      | 2     | 8     | 8     | 2     |                                      |
|      |A      |A      |A      |A      |                                      |
|      |       |       |       |       |                                      |
|      |{0, -2}|{1, -2}|{2, -2}|{3, -2}|                                      |
|      +-------+-------+-------+-------+                                      |
|                                                                             |
|o10 : SpectralSequencePage                                                   |
+-----------------------------------------------------------------------------+
|i11 : E'' ^1                                                                 |
|                                                                             |
|      +--------------------------+-------------------------------------------|
|o11 = |cokernel {-3} | z  y  x  ||cokernel {-1} | z  y  x  0  0  0  0  0  0  |
|      |         {-3} | -w -z -y ||         {0}  | 0  0  0  z  y  x  0  0  0  |
|      |                          |         {0}  | 0  0  0  0  0  0  z  y  x  |
|      |{0, -2}                   |         {0}  | 0  0  0  0  0  0  0  0  0  |
|      |                          |         {-1} | -w -z -y 0  0  0  0  0  0  |
|      |                          |         {0}  | 0  0  0  -w -z -y 0  0  0  |
|      |                          |         {0}  | 0  0  0  0  0  0  -w -z -y |
|      |                          |         {0}  | 0  0  0  0  0  0  0  0  0  |
|      |                          |                                           |
|      |                          |{1, -2}                                    |
|      +--------------------------+-------------------------------------------|
|                                                                             |
|o11 : SpectralSequencePage                                                   |
|-----------------------------------------------------------------------------|
|----------+----------------------------------------------------+-------------|
|0  0  0  ||cokernel {1} | z  y  x  0  0  0  0  0  0  0  0  0  ||cokernel {2} |
|0  0  0  ||         {1} | 0  0  0  z  y  x  0  0  0  0  0  0  ||         {2} |
|0  0  0  ||         {1} | 0  0  0  0  0  0  z  y  x  0  0  0  ||             |
|z  y  x  ||         {1} | 0  0  0  0  0  0  0  0  0  z  y  x  ||{3, -2}      |
|0  0  0  ||         {1} | -w -z -y 0  0  0  0  0  0  0  0  0  ||             |
|0  0  0  ||         {1} | 0  0  0  -w -z -y 0  0  0  0  0  0  ||             |
|0  0  0  ||         {1} | 0  0  0  0  0  0  -w -z -y 0  0  0  ||             |
|-w -z -y ||         {1} | 0  0  0  0  0  0  0  0  0  -w -z -y ||             |
|          |                                                    |             |
|          |{2, -2}                                             |             |
|----------+----------------------------------------------------+-------------|
|-----------------------------------------------------------------------------|
|------------+                                                                |
|| z  y  x  ||                                                                |
|| -w -z -y ||                                                                |
|            |                                                                |
|            |                                                                |
|            |                                                                |
|            |                                                                |
|            |                                                                |
|            |                                                                |
|            |                                                                |
|            |                                                                |
|------------+                                                                |
+-----------------------------------------------------------------------------+
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:1328:0.

Filtrations and tensor product complexes
****************************************

Let $S$ be a commutative ring and let $B : \dots \rightarrow B_{i} \rightarrow
B_{i - 1} \rightarrow \dots $ and $C : \dots \rightarrow C_{i} \rightarrow C_{i
- 1} \rightarrow \dots $ be chain complexes.

For all integers $p$ and $q$ let $K_{p,q} := B_p \otimes_S C_q$, let $d'_{p,q}
: K_{p,q} \rightarrow K_{p - 1, q}$ denote the homorphism $\partial^B_{p}
\otimes 1$, and let $d''_{p,q} : K_{p,q} \rightarrow K_{p, q - 1} $ denote the
homorphism $(-1)^p \otimes \partial_q^C $.

The chain complex $B \otimes_S C$ is given by $ (B \otimes_S C)_k := \oplus_{p
+ q = k} B_p \otimes_S C_q$ and the differentials by $\partial := d' + d''$. It
carries two natural ascending filtrations $F'B \otimes_S C$ and $F'' B
\otimes_S C$.

The first is obtained by letting $F'_n (B \otimes_S C)$ be the chain complex
determined by setting $F'_n (B \otimes_S C)_k := \oplus_{p + q = k , p \leq n}
B_{p} \otimes_S C_q$ and the differentials $\partial := d' + d''$.

The second is obtained by letting $F''_n (B \otimes_S C)$ be the chain complex
determined by setting $F''_n (B \otimes_S C)_k := \oplus_{p + q = k , q \leq n}
B_{p} \otimes_S C_q$ and the differentials $\partial := d' + d''$.

In Macaulay2 we can compute these filtered complexes as follows.

+-----------------------------------------------------------------------------+
|i1 : A = QQ[x,y,z,w];                                                        |
+-----------------------------------------------------------------------------+
|i2 : B = res monomialCurveIdeal(A,{1,2,3});                                  |
+-----------------------------------------------------------------------------+
|i3 : C = res monomialCurveIdeal(A,{1,3,4});                                  |
+-----------------------------------------------------------------------------+
|i4 : F' = (filteredComplex B) ** C                                           |
|                                                                             |
|o4 = -1 : image 0 <-- image 0 <-- image 0 <-- image 0 <-- image 0 <-- image 0|
|                                                                             |
|          0           1           2           3           4           5      |
|                                                                             |
|     0 : image | 1 | <-- image {2} | 1 0 0 0 0 0 0 | <-- image {4} | 1 0 0 0 |
|                               {3} | 0 1 0 0 0 0 0 |           {4} | 0 1 0 0 |
|         0                     {3} | 0 0 1 0 0 0 0 |           {4} | 0 0 1 0 |
|                               {3} | 0 0 0 1 0 0 0 |           {4} | 0 0 0 1 |
|                               {2} | 0 0 0 0 0 0 0 |           {4} | 0 0 0 0 |
|                               {2} | 0 0 0 0 0 0 0 |           {5} | 0 0 0 0 |
|                               {2} | 0 0 0 0 0 0 0 |           {5} | 0 0 0 0 |
|                                                               {5} | 0 0 0 0 |
|                         1                                     {4} | 0 0 0 0 |
|                                                               {5} | 0 0 0 0 |
|                                                               {5} | 0 0 0 0 |
|                                                               {5} | 0 0 0 0 |
|                                                               {4} | 0 0 0 0 |
|                                                               {5} | 0 0 0 0 |
|                                                               {5} | 0 0 0 0 |
|                                                               {5} | 0 0 0 0 |
|                                                               {3} | 0 0 0 0 |
|                                                               {3} | 0 0 0 0 |
|                                                                             |
|                                                         2                   |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|     1 : image | 1 | <-- image {2} | 1 0 0 0 0 0 0 | <-- image {4} | 1 0 0 0 |
|                               {3} | 0 1 0 0 0 0 0 |           {4} | 0 1 0 0 |
|         0                     {3} | 0 0 1 0 0 0 0 |           {4} | 0 0 1 0 |
|                               {3} | 0 0 0 1 0 0 0 |           {4} | 0 0 0 1 |
|                               {2} | 0 0 0 0 1 0 0 |           {4} | 0 0 0 0 |
|                               {2} | 0 0 0 0 0 1 0 |           {5} | 0 0 0 0 |
|                               {2} | 0 0 0 0 0 0 1 |           {5} | 0 0 0 0 |
|                                                               {5} | 0 0 0 0 |
|                         1                                     {4} | 0 0 0 0 |
|                                                               {5} | 0 0 0 0 |
|                                                               {5} | 0 0 0 0 |
|                                                               {5} | 0 0 0 0 |
|                                                               {4} | 0 0 0 0 |
|                                                               {5} | 0 0 0 0 |
|                                                               {5} | 0 0 0 0 |
|                                                               {5} | 0 0 0 0 |
|                                                               {3} | 0 0 0 0 |
|                                                               {3} | 0 0 0 0 |
|                                                                             |
|                                                         2                   |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|          1      7      18      21      11      2                            |
|     2 : A  <-- A  <-- A   <-- A   <-- A   <-- A  <-- 0 <-- 0                |
|                                                                             |
|         0      1      2       3       4       5      6     7                |
|                                                                             |
|o4 : FilteredComplex                                                         |
|-----------------------------------------------------------------------------|
| <-- image 0 <-- image 0                                                     |
|                                                                             |
|     6           7                                                           |
|                                                                             |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 | <-- image {5} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                                        {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                                        {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                                        {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                                                                             |
|                                  3                                          |
|                                                                             |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 | <-- image {5} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {6} | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {6} | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {6} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0|
|1 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {6} | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0|
|0 1 0 0 0 0 0 0 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0|
|0 0 1 0 0 0 0 0 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0|
|0 0 0 1 0 0 0 0 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0|
|0 0 0 0 1 0 0 0 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0|
|0 0 0 0 0 1 0 0 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0|
|0 0 0 0 0 0 1 0 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0|
|0 0 0 0 0 0 0 1 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0|
|0 0 0 0 0 0 0 0 1 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0|
|0 0 0 0 0 0 0 0 0 1 0 0 0 0 |           {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 1 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 1 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                                        {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                                        {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                                        {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                                                                             |
|                                  3                                          |
|-----------------------------------------------------------------------------|
|0 0 0 0 0 | <-- image 0 <-- image 0 <-- image 0 <-- image 0                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |     4           5           6           7                        |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|                                                                             |
|                                                                             |
|                                                                             |
|0 0 0 0 0 | <-- image {7} | 1 0 0 0 0 0 0 0 0 0 0 | <-- image 0 <-- image 0  |
|0 0 0 0 0 |           {7} | 0 1 0 0 0 0 0 0 0 0 0 |                          |
|0 0 0 0 0 |           {7} | 0 0 1 0 0 0 0 0 0 0 0 |     5           6        |
|0 0 0 0 0 |           {7} | 0 0 0 0 0 0 0 0 0 0 0 |                          |
|0 0 0 0 0 |           {7} | 0 0 0 0 0 0 0 0 0 0 0 |                          |
|0 0 0 0 0 |           {7} | 0 0 0 0 0 0 0 0 0 0 0 |                          |
|0 0 0 0 0 |           {7} | 0 0 0 0 0 0 0 0 0 0 0 |                          |
|0 0 0 0 0 |           {7} | 0 0 0 0 0 0 0 0 0 0 0 |                          |
|0 0 0 0 0 |           {7} | 0 0 0 0 0 0 0 0 0 0 0 |                          |
|0 0 0 0 0 |           {7} | 0 0 0 0 0 0 0 0 0 0 0 |                          |
|0 0 0 0 0 |           {7} | 0 0 0 0 0 0 0 0 0 0 0 |                          |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |     4                                                            |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|-----------------------------------------------------------------------------|
|<-- image 0                                                                  |
|                                                                             |
|    7                                                                        |
+-----------------------------------------------------------------------------+
|i5 : F'' = B ** (filteredComplex C)                                          |
|                                                                             |
|o5 = -1 : image 0 <-- image 0 <-- image 0 <-- image 0 <-- image 0 <-- image 0|
|                                                                             |
|          0           1           2           3           4           5      |
|                                                                             |
|     0 : image | 1 | <-- image {2} | 0 0 0 0 0 0 0 | <-- image {4} | 0 0 0 0 |
|                               {3} | 0 0 0 0 0 0 0 |           {4} | 0 0 0 0 |
|         0                     {3} | 0 0 0 0 0 0 0 |           {4} | 0 0 0 0 |
|                               {3} | 0 0 0 0 0 0 0 |           {4} | 0 0 0 0 |
|                               {2} | 0 0 0 0 1 0 0 |           {4} | 0 0 0 0 |
|                               {2} | 0 0 0 0 0 1 0 |           {5} | 0 0 0 0 |
|                               {2} | 0 0 0 0 0 0 1 |           {5} | 0 0 0 0 |
|                                                               {5} | 0 0 0 0 |
|                         1                                     {4} | 0 0 0 0 |
|                                                               {5} | 0 0 0 0 |
|                                                               {5} | 0 0 0 0 |
|                                                               {5} | 0 0 0 0 |
|                                                               {4} | 0 0 0 0 |
|                                                               {5} | 0 0 0 0 |
|                                                               {5} | 0 0 0 0 |
|                                                               {5} | 0 0 0 0 |
|                                                               {3} | 0 0 0 0 |
|                                                               {3} | 0 0 0 0 |
|                                                                             |
|                                                         2                   |
|                                                                             |
|     1 : image | 1 | <-- image {2} | 1 0 0 0 0 0 0 | <-- image {4} | 0 0 0 0 |
|                               {3} | 0 1 0 0 0 0 0 |           {4} | 0 0 0 0 |
|         0                     {3} | 0 0 1 0 0 0 0 |           {4} | 0 0 0 0 |
|                               {3} | 0 0 0 1 0 0 0 |           {4} | 0 0 0 0 |
|                               {2} | 0 0 0 0 1 0 0 |           {4} | 0 0 0 0 |
|                               {2} | 0 0 0 0 0 1 0 |           {5} | 0 0 0 0 |
|                               {2} | 0 0 0 0 0 0 1 |           {5} | 0 0 0 0 |
|                                                               {5} | 0 0 0 0 |
|                         1                                     {4} | 0 0 0 0 |
|                                                               {5} | 0 0 0 0 |
|                                                               {5} | 0 0 0 0 |
|                                                               {5} | 0 0 0 0 |
|                                                               {4} | 0 0 0 0 |
|                                                               {5} | 0 0 0 0 |
|                                                               {5} | 0 0 0 0 |
|                                                               {5} | 0 0 0 0 |
|                                                               {3} | 0 0 0 0 |
|                                                               {3} | 0 0 0 0 |
|                                                                             |
|                                                         2                   |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|     2 : image | 1 | <-- image {2} | 1 0 0 0 0 0 0 | <-- image {4} | 1 0 0 0 |
|                               {3} | 0 1 0 0 0 0 0 |           {4} | 0 1 0 0 |
|         0                     {3} | 0 0 1 0 0 0 0 |           {4} | 0 0 1 0 |
|                               {3} | 0 0 0 1 0 0 0 |           {4} | 0 0 0 1 |
|                               {2} | 0 0 0 0 1 0 0 |           {4} | 0 0 0 0 |
|                               {2} | 0 0 0 0 0 1 0 |           {5} | 0 0 0 0 |
|                               {2} | 0 0 0 0 0 0 1 |           {5} | 0 0 0 0 |
|                                                               {5} | 0 0 0 0 |
|                         1                                     {4} | 0 0 0 0 |
|                                                               {5} | 0 0 0 0 |
|                                                               {5} | 0 0 0 0 |
|                                                               {5} | 0 0 0 0 |
|                                                               {4} | 0 0 0 0 |
|                                                               {5} | 0 0 0 0 |
|                                                               {5} | 0 0 0 0 |
|                                                               {5} | 0 0 0 0 |
|                                                               {3} | 0 0 0 0 |
|                                                               {3} | 0 0 0 0 |
|                                                                             |
|                                                         2                   |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|          1      7      18      21      11      2                            |
|     3 : A  <-- A  <-- A   <-- A   <-- A   <-- A  <-- 0 <-- 0                |
|                                                                             |
|         0      1      2       3       4       5      6     7                |
|                                                                             |
|o5 : FilteredComplex                                                         |
|-----------------------------------------------------------------------------|
| <-- image 0 <-- image 0                                                     |
|                                                                             |
|     6           7                                                           |
|                                                                             |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 | <-- image 0 <-- image 0 <-- image 0 <-- image 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                                |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |     3           4           5           6      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                                |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                                |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                                |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                                |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                                |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                                |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                                |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                                |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                                |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                                |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                                |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                                |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                                |
|0 0 0 0 0 0 0 0 0 0 0 0 1 0 |                                                |
|0 0 0 0 0 0 0 0 0 0 0 0 0 1 |                                                |
|                                                                             |
|                                                                             |
|                                                                             |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 | <-- image {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|1 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 1 0 0 0 0 0 0 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 1 0 0 0 0 0 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 1 0 0 0 0 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 1 0 0 0 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 1 0 0 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 1 0 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 1 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 1 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 1 0 0 0 0 |           {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0|
|0 0 0 0 0 0 0 0 0 0 1 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0|
|0 0 0 0 0 0 0 0 0 0 0 1 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1|
|0 0 0 0 0 0 0 0 0 0 0 0 1 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 1 |           {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                                        {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                                        {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                                        {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                                                                             |
|                                  3                                          |
|                                                                             |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 | <-- image {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {6} | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {6} | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {6} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0|
|1 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {6} | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0|
|0 1 0 0 0 0 0 0 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0|
|0 0 1 0 0 0 0 0 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0|
|0 0 0 1 0 0 0 0 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0|
|0 0 0 0 1 0 0 0 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0|
|0 0 0 0 0 1 0 0 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0|
|0 0 0 0 0 0 1 0 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0|
|0 0 0 0 0 0 0 1 0 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0|
|0 0 0 0 0 0 0 0 1 0 0 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0|
|0 0 0 0 0 0 0 0 0 1 0 0 0 0 |           {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0|
|0 0 0 0 0 0 0 0 0 0 1 0 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0|
|0 0 0 0 0 0 0 0 0 0 0 1 0 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1|
|0 0 0 0 0 0 0 0 0 0 0 0 1 0 |           {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 1 |           {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                                        {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                                        {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                                        {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                                                                             |
|                                  3                                          |
|-----------------------------------------------------------------------------|
|<-- image 0                                                                  |
|                                                                             |
|    7                                                                        |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0 0 0 0 0 | <-- image 0 <-- image 0 <-- image 0 <-- image 0                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |     4           5           6           7                        |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|1 0 0 0 0 |                                                                  |
|0 1 0 0 0 |                                                                  |
|0 0 1 0 0 |                                                                  |
|0 0 0 1 0 |                                                                  |
|0 0 0 0 1 |                                                                  |
|                                                                             |
|                                                                             |
|                                                                             |
|0 0 0 0 0 | <-- image {7} | 0 0 0 0 0 0 0 0 0 0 0 | <-- image 0 <-- image 0  |
|0 0 0 0 0 |           {7} | 0 0 0 0 0 0 0 0 0 0 0 |                          |
|0 0 0 0 0 |           {7} | 0 0 0 0 0 0 0 0 0 0 0 |     5           6        |
|0 0 0 0 0 |           {7} | 0 0 0 1 0 0 0 0 0 0 0 |                          |
|0 0 0 0 0 |           {7} | 0 0 0 0 1 0 0 0 0 0 0 |                          |
|0 0 0 0 0 |           {7} | 0 0 0 0 0 1 0 0 0 0 0 |                          |
|0 0 0 0 0 |           {7} | 0 0 0 0 0 0 1 0 0 0 0 |                          |
|0 0 0 0 0 |           {7} | 0 0 0 0 0 0 0 1 0 0 0 |                          |
|0 0 0 0 0 |           {7} | 0 0 0 0 0 0 0 0 1 0 0 |                          |
|0 0 0 0 0 |           {7} | 0 0 0 0 0 0 0 0 0 1 0 |                          |
|0 0 0 0 0 |           {7} | 0 0 0 0 0 0 0 0 0 0 1 |                          |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |     4                                                            |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|0 0 0 0 0 |                                                                  |
|1 0 0 0 0 |                                                                  |
|0 1 0 0 0 |                                                                  |
|0 0 1 0 0 |                                                                  |
|0 0 0 1 0 |                                                                  |
|0 0 0 0 1 |                                                                  |
|-----------------------------------------------------------------------------|
|<-- image 0                                                                  |
|                                                                             |
|    7                                                                        |
+-----------------------------------------------------------------------------+

The pages of the resulting spectral sequences take the form:

+-----------------------------------------------------------------------------+
|i6 : E' = prune spectralSequence F';                                         |
+-----------------------------------------------------------------------------+
|i7 : E'' = prune spectralSequence F'';                                       |
+-----------------------------------------------------------------------------+
|i8 : E' ^0                                                                   |
|                                                                             |
|     +------+------+------+                                                  |
|     | 1    | 3    | 2    |                                                  |
|o8 = |A     |A     |A     |                                                  |
|     |      |      |      |                                                  |
|     |{0, 3}|{1, 3}|{2, 3}|                                                  |
|     +------+------+------+                                                  |
|     | 4    | 12   | 8    |                                                  |
|     |A     |A     |A     |                                                  |
|     |      |      |      |                                                  |
|     |{0, 2}|{1, 2}|{2, 2}|                                                  |
|     +------+------+------+                                                  |
|     | 4    | 12   | 8    |                                                  |
|     |A     |A     |A     |                                                  |
|     |      |      |      |                                                  |
|     |{0, 1}|{1, 1}|{2, 1}|                                                  |
|     +------+------+------+                                                  |
|     | 1    | 3    | 2    |                                                  |
|     |A     |A     |A     |                                                  |
|     |      |      |      |                                                  |
|     |{0, 0}|{1, 0}|{2, 0}|                                                  |
|     +------+------+------+                                                  |
|                                                                             |
|o8 : SpectralSequencePage                                                    |
+-----------------------------------------------------------------------------+
|i9 : E' ^ 1                                                                  |
|                                                                             |
|     +----------------------------------------+------------------------------|
|o9 = |cokernel | yz-xw z3-yw2 xz2-y2w y3-x2z ||cokernel {2} | yz-xw 0     0  |
|     |                                        |         {2} | 0     yz-xw 0  |
|     |{0, 0}                                  |         {2} | 0     0     yz-|
|     |                                        |                              |
|     |                                        |{1, 0}                        |
|     +----------------------------------------+------------------------------|
|                                                                             |
|o9 : SpectralSequencePage                                                    |
|-----------------------------------------------------------------------------|
|----------------------------------------------------------------------+------|
|   z3-yw2 xz2-y2w y3-x2z 0      0       0      0      0       0      ||cokern|
|   0      0       0      z3-yw2 xz2-y2w y3-x2z 0      0       0      ||      |
|xw 0      0       0      0      0       0      z3-yw2 xz2-y2w y3-x2z ||      |
|                                                                      |{2, 0}|
|                                                                      |      |
|----------------------------------------------------------------------+------|
|-----------------------------------------------------------------------------|
|------------------------------------------------------------------+          |
|el {3} | yz-xw 0     z3-yw2 xz2-y2w y3-x2z 0      0       0      ||          |
|   {3} | 0     yz-xw 0      0       0      z3-yw2 xz2-y2w y3-x2z ||          |
|                                                                  |          |
|                                                                  |          |
|                                                                  |          |
|------------------------------------------------------------------+          |
+-----------------------------------------------------------------------------+
|i10 : E'' ^0                                                                 |
|                                                                             |
|      +------+------+------+------+                                          |
|      | 2    | 8    | 8    | 2    |                                          |
|o10 = |A     |A     |A     |A     |                                          |
|      |      |      |      |      |                                          |
|      |{0, 2}|{1, 2}|{2, 2}|{3, 2}|                                          |
|      +------+------+------+------+                                          |
|      | 3    | 12   | 12   | 3    |                                          |
|      |A     |A     |A     |A     |                                          |
|      |      |      |      |      |                                          |
|      |{0, 1}|{1, 1}|{2, 1}|{3, 1}|                                          |
|      +------+------+------+------+                                          |
|      | 1    | 4    | 4    | 1    |                                          |
|      |A     |A     |A     |A     |                                          |
|      |      |      |      |      |                                          |
|      |{0, 0}|{1, 0}|{2, 0}|{3, 0}|                                          |
|      +------+------+------+------+                                          |
|                                                                             |
|o10 : SpectralSequencePage                                                   |
+-----------------------------------------------------------------------------+
|i11 : E'' ^1                                                                 |
|                                                                             |
|      +------------------------------+---------------------------------------|
|o11 = |cokernel | z2-yw yz-xw y2-xz ||cokernel {2} | z2-yw yz-xw y2-xz 0     |
|      |                              |         {3} | 0     0     0     z2-yw |
|      |{0, 0}                        |         {3} | 0     0     0     0     |
|      |                              |         {3} | 0     0     0     0     |
|      |                              |                                       |
|      |                              |{1, 0}                                 |
|      +------------------------------+---------------------------------------|
|                                                                             |
|o11 : SpectralSequencePage                                                   |
|-----------------------------------------------------------------------------|
|-------------------------------------------------+---------------------------|
|0     0     0     0     0     0     0     0     ||cokernel {4} | z2-yw yz-xw |
|yz-xw y2-xz 0     0     0     0     0     0     ||         {4} | 0     0     |
|0     0     z2-yw yz-xw y2-xz 0     0     0     ||         {4} | 0     0     |
|0     0     0     0     0     z2-yw yz-xw y2-xz ||         {4} | 0     0     |
|                                                 |                           |
|                                                 |{2, 0}                     |
|-------------------------------------------------+---------------------------|
|-----------------------------------------------------------------------------|
|-------------------------------------------------------------+---------------|
|y2-xz 0     0     0     0     0     0     0     0     0     ||cokernel {5} | |
|0     z2-yw yz-xw y2-xz 0     0     0     0     0     0     ||               |
|0     0     0     0     z2-yw yz-xw y2-xz 0     0     0     ||{3, 0}         |
|0     0     0     0     0     0     0     z2-yw yz-xw y2-xz ||               |
|                                                             |               |
|                                                             |               |
|-------------------------------------------------------------+---------------|
|-----------------------------------------------------------------------------|
|-------------------+                                                         |
|z2-yw yz-xw y2-xz ||                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|-------------------+                                                         |
+-----------------------------------------------------------------------------+

See also
========

  * Balancing Tor
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:1381:0.

hilbertPolynomial(SpectralSequencePage) -- the Hilbert polynomial of a spectral sequence page
*********************************************************************************************

  * Function: hilbertPolynomial (Macaulay2Doc),
  * Usage:
        H = hilbertPolynomial(E)
  * Inputs:
      * E, a spectral sequence page,
  * Optional inputs (Macaulay2Doc),:
      * Projective (Macaulay2Doc),
        => ..., default value true,
  * Outputs:
      * H, a Page,

Description
===========

Returns the Hilbert polynomials of all modules of the spectral sequence page

As a specific example consider the filtered complex $K$ below, obtained by
multiplying the minimal free resolution of the rational quartic space curve by
successive powers of the irrelevant ideal.

+----------------------------------------------------+
|i1 : B = QQ[a..d];                                  |
+----------------------------------------------------+
|i2 : J = ideal vars B;                              |
|                                                    |
|o2 : Ideal of B                                     |
+----------------------------------------------------+
|i3 : C = complete res monomialCurveIdeal(B,{1,3,4});|
+----------------------------------------------------+
|i4 : K = filteredComplex(J,C,4);                    |
+----------------------------------------------------+

We compute the degree $0$ piece of the $E^3$ page below.

+----------------------------------+
|i5 : E = prune spectralSequence K;|
+----------------------------------+
|i6 : hilbertPolynomial(E^3)       |
|                                  |
|     +-------------+              |
|o6 = |- 3*P  + 4*P |              |
|     |     0      1|              |
|     |             |              |
|     |{-4, 4}      |              |
|     +-------------+              |
|                                  |
|o6 : Page                         |
+----------------------------------+

Ways to use this method:
========================

  * hilbertPolynomial(SpectralSequencePage)
    -- the Hilbert polynomial of a
    spectral sequence page
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:3056:0.

Hom(FilteredComplex,ChainComplex) -- the filtered Hom complex
*************************************************************

  * Function: Hom (Macaulay2Doc),
  * Usage:
        f = Hom(K,C)
  * Inputs:
      * K, a filtered chain complex,
      * C, a chain complex (OldChainComplexes),
  * Optional inputs (Macaulay2Doc),:
      * DegreeLimit (Macaulay2Doc), => ..., default value null,
      * MinimalGenerators (Macaulay2Doc), => ..., default value true,
      * Strategy (Macaulay2Doc), => ..., default value null,
  * Outputs:
      * f, a filtered chain complex,

Description
===========

Returns the filtrations of the Hom complex determined by the double complex.
Here is an example which illustrates the syntax.

+-----------------------------------------------------------------------------+
|i1 : A = QQ[x,y,z,w];                                                        |
+-----------------------------------------------------------------------------+
|i2 : B = res monomialCurveIdeal(A, {1,2,3});                                 |
+-----------------------------------------------------------------------------+
|i3 : C = res monomialCurveIdeal(A, {1,3,4});                                 |
+-----------------------------------------------------------------------------+
|i4 : F' = Hom(filteredComplex B, C)                                          |
|                                                                             |
|o4 = -3 : image 0 <-- image 0 <-- image 0 <-- image 0 <-- image 0 <-- image 0|
|                                                                             |
|          -3          -2          -1          0           1           2      |
|                                                                             |
|     -2 : image 0 <-- image {-3} | 1 0 | <-- image {-2} | 0 0 0 0 0 0 0 0 0 0|
|                            {-3} | 0 1 |           {-2} | 0 0 0 0 0 0 0 0 0 0|
|          -3                                       {-2} | 0 0 0 0 0 0 0 0 0 0|
|                      -2                           {-1} | 0 0 0 1 0 0 0 0 0 0|
|                                                   {0}  | 0 0 0 0 1 0 0 0 0 0|
|                                                   {0}  | 0 0 0 0 0 1 0 0 0 0|
|                                                   {0}  | 0 0 0 0 0 0 1 0 0 0|
|                                                   {-1} | 0 0 0 0 0 0 0 1 0 0|
|                                                   {0}  | 0 0 0 0 0 0 0 0 1 0|
|                                                   {0}  | 0 0 0 0 0 0 0 0 0 1|
|                                                   {0}  | 0 0 0 0 0 0 0 0 0 0|
|                                                                             |
|                                             -1                              |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|     -1 : image 0 <-- image {-3} | 1 0 | <-- image {-2} | 1 0 0 0 0 0 0 0 0 0|
|                            {-3} | 0 1 |           {-2} | 0 1 0 0 0 0 0 0 0 0|
|          -3                                       {-2} | 0 0 1 0 0 0 0 0 0 0|
|                      -2                           {-1} | 0 0 0 1 0 0 0 0 0 0|
|                                                   {0}  | 0 0 0 0 1 0 0 0 0 0|
|                                                   {0}  | 0 0 0 0 0 1 0 0 0 0|
|                                                   {0}  | 0 0 0 0 0 0 1 0 0 0|
|                                                   {-1} | 0 0 0 0 0 0 0 1 0 0|
|                                                   {0}  | 0 0 0 0 0 0 0 0 1 0|
|                                                   {0}  | 0 0 0 0 0 0 0 0 0 1|
|                                                   {0}  | 0 0 0 0 0 0 0 0 0 0|
|                                                                             |
|                                             -1                              |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                 2      11      21      18      7      1                     |
|     0 : 0  <-- A  <-- A   <-- A   <-- A   <-- A  <-- A  <-- 0               |
|                                                                             |
|         -3     -2     -1      0       1       2      3      4               |
|                                                                             |
|o4 : FilteredComplex                                                         |
|-----------------------------------------------------------------------------|
|<-- image 0 <-- image 0                                                      |
|                                                                             |
|    3           4                                                            |
|                                                                             |
|0 | <-- image {0} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | <-- image {2}|
|0 |           {0} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {3}|
|0 |           {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {3}|
|0 |           {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {3}|
|0 |           {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {2}|
|0 |           {0} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {2}|
|0 |           {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {2}|
|0 |           {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {2}|
|0 |           {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {2}|
|0 |           {0} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {2}|
|1 |           {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {2}|
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {2}|
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {2}|
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 |           {2}|
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 |           {2}|
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 |           {2}|
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 |           {2}|
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 |           {2}|
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 |     1        |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 |              |
|                                                                             |
|        0                                                                    |
|                                                                             |
|0 | <-- image {0} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | <-- image {2}|
|0 |           {0} | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {3}|
|0 |           {1} | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {3}|
|0 |           {1} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {3}|
|0 |           {1} | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {2}|
|0 |           {0} | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {2}|
|0 |           {1} | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {2}|
|0 |           {1} | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {2}|
|0 |           {1} | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |           {2}|
|0 |           {0} | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |           {2}|
|1 |           {1} | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 |           {2}|
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 |           {2}|
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 |           {2}|
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 |           {2}|
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 |           {2}|
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 |           {2}|
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 |           {2}|
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 |           {2}|
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 |     1        |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 |              |
|                                                                             |
|        0                                                                    |
|-----------------------------------------------------------------------------|
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | <-- image 0 <-- image 0 <-- image 0  |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |     2           3           4        |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 |                                      |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | <-- image {4} | 0 0 0 0 0 0 0 | <--  |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {4} | 0 0 0 0 0 0 0 |      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {4} | 0 0 0 0 0 0 0 |      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {4} | 0 0 0 0 0 0 0 |      |
|| 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {3} | 0 0 0 0 1 0 0 |      |
|| 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |           {3} | 0 0 0 0 0 1 0 |      |
|| 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |           {3} | 0 0 0 0 0 0 1 |      |
|| 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 |     2                                |
|| 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 |                                      |
|| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 |                                      |
|-----------------------------------------------------------------------------|
|image 0 <-- image 0                                                          |
|                                                                             |
|3           4                                                                |
+-----------------------------------------------------------------------------+
|i5 : F'' = Hom(B,filteredComplex C)                                          |
|                                                                             |
|o5 = -1 : image 0 <-- image 0 <-- image 0 <-- image 0 <-- image 0 <-- image 0|
|                                                                             |
|          -3          -2          -1          0           1           2      |
|                                                                             |
|     0 : image 0 <-- image {-3} | 1 0 | <-- image {-2} | 1 0 0 0 0 0 0 0 0 0 |
|                           {-3} | 0 1 |           {-2} | 0 1 0 0 0 0 0 0 0 0 |
|         -3                                       {-2} | 0 0 1 0 0 0 0 0 0 0 |
|                     -2                           {-1} | 0 0 0 0 0 0 0 0 0 0 |
|                                                  {0}  | 0 0 0 0 0 0 0 0 0 0 |
|                                                  {0}  | 0 0 0 0 0 0 0 0 0 0 |
|                                                  {0}  | 0 0 0 0 0 0 0 0 0 0 |
|                                                  {-1} | 0 0 0 0 0 0 0 0 0 0 |
|                                                  {0}  | 0 0 0 0 0 0 0 0 0 0 |
|                                                  {0}  | 0 0 0 0 0 0 0 0 0 0 |
|                                                  {0}  | 0 0 0 0 0 0 0 0 0 0 |
|                                                                             |
|                                            -1                               |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|     1 : image 0 <-- image {-3} | 1 0 | <-- image {-2} | 1 0 0 0 0 0 0 0 0 0 |
|                           {-3} | 0 1 |           {-2} | 0 1 0 0 0 0 0 0 0 0 |
|         -3                                       {-2} | 0 0 1 0 0 0 0 0 0 0 |
|                     -2                           {-1} | 0 0 0 1 0 0 0 0 0 0 |
|                                                  {0}  | 0 0 0 0 1 0 0 0 0 0 |
|                                                  {0}  | 0 0 0 0 0 1 0 0 0 0 |
|                                                  {0}  | 0 0 0 0 0 0 1 0 0 0 |
|                                                  {-1} | 0 0 0 0 0 0 0 1 0 0 |
|                                                  {0}  | 0 0 0 0 0 0 0 0 1 0 |
|                                                  {0}  | 0 0 0 0 0 0 0 0 0 1 |
|                                                  {0}  | 0 0 0 0 0 0 0 0 0 0 |
|                                                                             |
|                                            -1                               |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|     2 : image 0 <-- image {-3} | 1 0 | <-- image {-2} | 1 0 0 0 0 0 0 0 0 0 |
|                           {-3} | 0 1 |           {-2} | 0 1 0 0 0 0 0 0 0 0 |
|         -3                                       {-2} | 0 0 1 0 0 0 0 0 0 0 |
|                     -2                           {-1} | 0 0 0 1 0 0 0 0 0 0 |
|                                                  {0}  | 0 0 0 0 1 0 0 0 0 0 |
|                                                  {0}  | 0 0 0 0 0 1 0 0 0 0 |
|                                                  {0}  | 0 0 0 0 0 0 1 0 0 0 |
|                                                  {-1} | 0 0 0 0 0 0 0 1 0 0 |
|                                                  {0}  | 0 0 0 0 0 0 0 0 1 0 |
|                                                  {0}  | 0 0 0 0 0 0 0 0 0 1 |
|                                                  {0}  | 0 0 0 0 0 0 0 0 0 0 |
|                                                                             |
|                                            -1                               |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                 2      11      21      18      7      1                     |
|     3 : 0  <-- A  <-- A   <-- A   <-- A   <-- A  <-- A  <-- 0               |
|                                                                             |
|         -3     -2     -1      0       1       2      3      4               |
|                                                                             |
|o5 : FilteredComplex                                                         |
|-----------------------------------------------------------------------------|
| <-- image 0 <-- image 0                                                     |
|                                                                             |
|     3           4                                                           |
|                                                                             |
|0 | <-- image {0} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | <-- image    |
|0 |           {0} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |     1        |
|0 |           {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {0} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {0} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|                                                                             |
|        0                                                                    |
|                                                                             |
|0 | <-- image {0} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | <-- image    |
|0 |           {0} | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {1} | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {1} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {1} | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {0} | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {1} | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {1} | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {1} | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {0} | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |              |
|1 |           {1} | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |     1        |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|                                                                             |
|        0                                                                    |
|                                                                             |
|0 | <-- image {0} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | <-- image    |
|0 |           {0} | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {1} | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {1} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {1} | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {0} | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {1} | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {1} | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {1} | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |              |
|0 |           {0} | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |              |
|1 |           {1} | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 |              |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 |     1        |
|              {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 |              |
|                                                                             |
|        0                                                                    |
|-----------------------------------------------------------------------------|
|0 <-- image 0 <-- image 0 <-- image 0                                        |
|                                                                             |
|      2           3           4                                              |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|{2} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | <-- image 0 <-- image 0 <--      |
|{3} | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                  |
|{3} | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |     2           3                |
|{3} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|{2} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | <-- image {4} | 1 0 0 0 0 0      |
|{3} | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {4} | 0 1 0 0 0 0      |
|{3} | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {4} | 0 0 1 0 0 0      |
|{3} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {4} | 0 0 0 1 0 0      |
|{2} | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {3} | 0 0 0 0 0 0      |
|{2} | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |           {3} | 0 0 0 0 0 0      |
|{2} | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |           {3} | 0 0 0 0 0 0      |
|{2} | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 |     2                            |
|{2} | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                  |
|{2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                  |
|-----------------------------------------------------------------------------|
|image 0                                                                      |
|                                                                             |
|4                                                                            |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0 | <-- image 0 <-- image 0                                                  |
|0 |                                                                          |
|0 |     3           4                                                        |
|0 |                                                                          |
|0 |                                                                          |
|0 |                                                                          |
|0 |                                                                          |
+-----------------------------------------------------------------------------+

See also
========

  * Filtrations and tensor product complexes

Ways to use this method:
========================

  * "Hom(ChainComplex,FilteredComplex)"
  * Hom(FilteredComplex,ChainComplex)
    -- the filtered Hom complex
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:3216:0.

homologyIsomorphism -- compute the homology isomorphism
*******************************************************

Description
===========

Computes the isomorphism $ker d^r_{p,q} / image d^r_{p + r, q - r + 1}
\rightarrow E^{r+1}_{p,q}$

See also
========

  * homologyIsomorphism(SpectralSequence,ZZ,ZZ,ZZ)
    -- the homology
    isomorphism

Ways to use homologyIsomorphism:
================================

  * homologyIsomorphism(SpectralSequence,ZZ,ZZ,ZZ)
    -- the homology
    isomorphism

For the programmer
==================

The object homologyIsomorphism, is a method function (Macaulay2Doc).

-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:3761:0.

homologyIsomorphism(SpectralSequence,ZZ,ZZ,ZZ) -- the homology isomorphism
**************************************************************************

  * Function: homologyIsomorphism,
  * Usage:
        g = homologyIsomorphism(SpectralSequence, ZZ, ZZ, ZZ)
  * Inputs:
      * E, a spectral sequence,
      * p, an integer (Macaulay2Doc),
      * q, an integer (Macaulay2Doc),
      * r, an integer (Macaulay2Doc),
  * Outputs:
      * g, a matrix (Macaulay2Doc),

Description
===========

Computes the isomorphism $ker d^r_{p,q} / image d^r_{p + r, q - r + 1}
\rightarrow E^{r+1}_{p,q}$

+-----------------------------------------------------------------------------+
|i1 : A = ZZ [s,t,u,v,w] ;                                                    |
+-----------------------------------------------------------------------------+
|i2 : K = filteredComplex(reverse {simplicialComplex {s}, simplicialComplex   |
|-----------------------------------------------------------------------------|
|{s,t}, simplicialComplex {s,t,u}, simplicialComplex {s*t, u},                |
|-----------------------------------------------------------------------------|
|simplicialComplex {s*t, u, v}, simplicialComplex {s*t, u, v, w},             |
|-----------------------------------------------------------------------------|
|simplicialComplex {s*t, s*w ,u, v}, simplicialComplex {s*t, s*w ,t * w, u,   |
|-----------------------------------------------------------------------------|
|v}, simplicialComplex {s*t, s*w ,t * w, u * v}, simplicialComplex {s*t, s*w  |
|-----------------------------------------------------------------------------|
|,t * w, u * v, s * v}, simplicialComplex {s*t, s*w ,t * w, u * v, s * v,     |
|-----------------------------------------------------------------------------|
|s*u}, simplicialComplex {s*t, s*w ,t * w, u * v, s * v, s*u, u * w},         |
|-----------------------------------------------------------------------------|
|simplicialComplex {s*t, s*w ,t * w, u * v, s * v, s*u, u * w, t* u},         |
|-----------------------------------------------------------------------------|
|simplicialComplex {s*t, s*w ,t * w, u * v, s * v, s*u, u * w, t* u, t*u*w},  |
|-----------------------------------------------------------------------------|
|simplicialComplex {s*t, s*w ,t * w, u * v, s * v, s*u, u * w, t* u, t*u*w,   |
|-----------------------------------------------------------------------------|
|s*u*w}, simplicialComplex {s*t, s*w ,t * w, u * v, s * v, s*u, u * w, t* u,  |
|-----------------------------------------------------------------------------|
|t*u*w, s*u*w,s*t*u}, simplicialComplex {s*t, s*w ,t * w, u * v, s * v, s*u, u|
|-----------------------------------------------------------------------------|
|* w, t* u, t*u*w, s*u*w,s*t*u, s*u*v}, simplicialComplex {s*t, s*w ,t * w, u |
|-----------------------------------------------------------------------------|
|* v, s * v, s*u, u * w, t* u, t*u*w, s*u*w,s*t*u, s*u*v, s*t*w}},            |
|-----------------------------------------------------------------------------|
|ReducedHomology => false);                                                   |
+-----------------------------------------------------------------------------+
|i3 : E = prune spectralSequence K                                            |
|                                                                             |
|o3 = E                                                                       |
|                                                                             |
|o3 : SpectralSequence                                                        |
+-----------------------------------------------------------------------------+
|i4 : e = spectralSequence K                                                  |
|                                                                             |
|o4 = e                                                                       |
|                                                                             |
|o4 : SpectralSequence                                                        |
+-----------------------------------------------------------------------------+
|i5 : apply(keys support E^11, i -> homologyIsomorphism(E, i#0, i#1, 11))     |
|                                                                             |
|o5 = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,|
|     ------------------------------------------------------------------------|
|     0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, | 1 |, 0,|
|     ------------------------------------------------------------------------|
|     0, 0, | 1 |, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,|
|     ------------------------------------------------------------------------|
|     0, 0, 0, 0, 0, 0}                                                       |
|                                                                             |
|o5 : List                                                                    |
+-----------------------------------------------------------------------------+
|i6 : apply(keys support e^11, i -> homologyIsomorphism(e, i#0, i#1, 11))     |
|                                                                             |
|o6 = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|     ------------------------------------------------------------------------|
|     0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, | 1 0 0 0|
|                                                                    | 0 0 0 0|
|                                                                    | 0 0 0 0|
|                                                                    | 0 0 0 0|
|                                                                    | 0 0 0 0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|     ------------------------------------------------------------------------|
|     0 |, 0, 0, 0, | 1 0 0 0 0 0 0 0 0 0 0 0 |, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,|
|     0 |           | 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|     0 |           | 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|     0 |           | 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|     0 |           | 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|                   | 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|                   | 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|                   | 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|                   | 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|                   | 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|                   | 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|                   | 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|                   | 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|     ------------------------------------------------------------------------|
|     0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}                         |
|                                                                             |
|o6 : List                                                                    |
+-----------------------------------------------------------------------------+

See also
========

  * homologyIsomorphism -- compute the homology
    isomorphism

Ways to use this method:
========================

  * homologyIsomorphism(SpectralSequence,ZZ,ZZ,ZZ)
    -- the homology
    isomorphism
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:3790:0.

How to make filtered complexes from chain complex maps
******************************************************

We describe the most primitive way to create filtered complexes.

Let $C$ be a chain complex and consider a list of chain complex maps $\{\phi_n,
\phi_{n - 1}, \dots, \phi_0  \}$ with properties that $C$ is the target of
$\phi_i$, for $0 \leq i \leq n$, and the image of $\phi_{i-1}$ is a subchain
complex of the image of $\phi_i$, for $1 \leq i \leq n$. Given this input data
we produce an ascending filtered chain complex $FC$ with the properties that
$F_k C = C$ for $k \geq n + 1$ and $F_k C = image \phi_k$, for $k = 0, \dots,
n$.

We now illustrate how this is done in two easy examples. We first make three
chain complexes $C$, $D$, and $E$, two chain complex maps, $d : D \rightarrow
C$ and $e : E \rightarrow C$, and then compute the resulting filtration of $C$.

Let's make our chain complexes $C$, $D$, and $E$.

+-----------------------------------------------------------------------------+
|i1 : R = QQ[x,y,z,w] ;                                                       |
+-----------------------------------------------------------------------------+
|i2 : c2 = matrix(R,{{1},{0}}) ;                                              |
|                                                                             |
|             2      1                                                        |
|o2 : Matrix R  <-- R                                                         |
+-----------------------------------------------------------------------------+
|i3 : c1 = matrix(R,{{0,1}}) ;                                                |
|                                                                             |
|             1      2                                                        |
|o3 : Matrix R  <-- R                                                         |
+-----------------------------------------------------------------------------+
|i4 : C = chainComplex({c1,c2})                                               |
|                                                                             |
|      1      2      1                                                        |
|o4 = R  <-- R  <-- R                                                         |
|                                                                             |
|     0      1      2                                                         |
|                                                                             |
|o4 : ChainComplex                                                            |
+-----------------------------------------------------------------------------+
|i5 : D_2 = image matrix(R,{{1}});                                            |
+-----------------------------------------------------------------------------+
|i6 : D_1 = image matrix(R,{{1,0},{0,0}});                                    |
+-----------------------------------------------------------------------------+
|i7 : D_0 = image matrix(R,{{1}});                                            |
+-----------------------------------------------------------------------------+
|i8 : D = chainComplex({inducedMap(D_0,D_1,C.dd_1),inducedMap(D_1,D_2,C.dd_2  |
|                                                                             |
|o8 = image | 1 | <-- image | 1 0 | <-- image | 1 |                           |
|                           | 0 0 |                                           |
|     0                                 2                                     |
|                     1                                                       |
|                                                                             |
|o8 : ChainComplex                                                            |
|-----------------------------------------------------------------------------|
|)})                                                                          |
+-----------------------------------------------------------------------------+
|i9 : E_2 = image matrix(R,{{0}});                                            |
+-----------------------------------------------------------------------------+
|i10 : E_1 = image matrix(R,{{1,0},{0,0}});                                   |
+-----------------------------------------------------------------------------+
|i11 : E_0 = image matrix(R,{{1}});                                           |
+-----------------------------------------------------------------------------+
|i12 : E = chainComplex({inducedMap(E_0,E_1,C.dd_1),inducedMap(E_1,E_2,C.dd_2 |
|                                                                             |
|o12 = image | 1 | <-- image | 1 0 | <-- image 0                              |
|                            | 0 0 |                                          |
|      0                                 2                                    |
|                      1                                                      |
|                                                                             |
|o12 : ChainComplex                                                           |
|-----------------------------------------------------------------------------|
|)})                                                                          |
+-----------------------------------------------------------------------------+

We now make our chain complex maps.

+-----------------------------------------------------------------------------+
|i13 : d = chainComplexMap(C,D,apply(spots C, i-> inducedMap(C_i,D_i,id_C     |
|                                                                             |
|           1                                                                 |
|o13 = 0 : R  <--------- image | 1 | : 0                                      |
|                | 1 |                                                        |
|                                                                             |
|           2                                                                 |
|      1 : R  <----------- image | 1 0 | : 1                                  |
|                | 1 0 |         | 0 0 |                                      |
|                | 0 0 |                                                      |
|                                                                             |
|           1                                                                 |
|      2 : R  <--------- image | 1 | : 2                                      |
|                | 1 |                                                        |
|                                                                             |
|o13 : ChainComplexMap                                                        |
|-----------------------------------------------------------------------------|
|_i)))                                                                        |
+-----------------------------------------------------------------------------+
|i14 : e = chainComplexMap(C,E,apply(spots C, i->inducedMap(C_i,E_i, id_C     |
|                                                                             |
|           1                                                                 |
|o14 = 0 : R  <--------- image | 1 | : 0                                      |
|                | 1 |                                                        |
|                                                                             |
|           2                                                                 |
|      1 : R  <----------- image | 1 0 | : 1                                  |
|                | 1 0 |         | 0 0 |                                      |
|                | 0 0 |                                                      |
|                                                                             |
|           1                                                                 |
|      2 : R  <----- image 0 : 2                                              |
|                0                                                            |
|                                                                             |
|o14 : ChainComplexMap                                                        |
|-----------------------------------------------------------------------------|
|_i)))                                                                        |
+-----------------------------------------------------------------------------+

We can check that these are indeed chain complex maps:

+-------------------------+
|i15 : isChainComplexMap d|
|                         |
|o15 = true               |
+-------------------------+
|i16 : isChainComplexMap e|
|                         |
|o16 = true               |
+-------------------------+

Now, given the list of chain complex maps $\{d, e\}$, we obtain a filtration of
$C$ by:

+-------------------------------------------------------+
|i17 : K = filteredComplex({d,e})                       |
|                                                       |
|o17 = -1 : image 0 <-- image 0 <-- image 0             |
|                                                       |
|           0           1           2                   |
|                                                       |
|      0 : image | 1 | <-- image | 1 0 | <-- image 0    |
|                                | 0 0 |                |
|          0                                 2          |
|                          1                            |
|                                                       |
|      1 : image | 1 | <-- image | 1 0 | <-- image | 1 ||
|                                | 0 0 |                |
|          0                                 2          |
|                          1                            |
|                                                       |
|           1      2      1                             |
|      2 : R  <-- R  <-- R                              |
|                                                       |
|          0      1      2                              |
|                                                       |
|o17 : FilteredComplex                                  |
+-------------------------------------------------------+

If we want to specify a minimum filtration degree we can use the Shift option.

+-------------------------------------------------------+
|i18 : L = filteredComplex({d,e},Shift =>1)             |
|                                                       |
|o18 = -2 : image 0 <-- image 0 <-- image 0             |
|                                                       |
|           0           1           2                   |
|                                                       |
|      -1 : image | 1 | <-- image | 1 0 | <-- image 0   |
|                                 | 0 0 |               |
|           0                                 2         |
|                           1                           |
|                                                       |
|      0 : image | 1 | <-- image | 1 0 | <-- image | 1 ||
|                                | 0 0 |                |
|          0                                 2          |
|                          1                            |
|                                                       |
|           1      2      1                             |
|      1 : R  <-- R  <-- R                              |
|                                                       |
|          0      1      2                              |
|                                                       |
|o18 : FilteredComplex                                  |
+-------------------------------------------------------+
|i19 : M = filteredComplex({d,e},Shift =>-1)            |
|                                                       |
|o19 = 0 : image 0 <-- image 0 <-- image 0              |
|                                                       |
|          0           1           2                    |
|                                                       |
|      1 : image | 1 | <-- image | 1 0 | <-- image 0    |
|                                | 0 0 |                |
|          0                                 2          |
|                          1                            |
|                                                       |
|      2 : image | 1 | <-- image | 1 0 | <-- image | 1 ||
|                                | 0 0 |                |
|          0                                 2          |
|                          1                            |
|                                                       |
|           1      2      1                             |
|      3 : R  <-- R  <-- R                              |
|                                                       |
|          0      1      2                              |
|                                                       |
|o19 : FilteredComplex                                  |
+-------------------------------------------------------+
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:1448:0.

I-adic filtrations of chain complexes and their spectral sequences
******************************************************************

By multiplying a chain complex by successive powers of an ideal we obtain a
filtered complex.

+-----------------------------------------------------------------------------+
|i1 : B = QQ[a..d]                                                            |
|                                                                             |
|o1 = B                                                                       |
|                                                                             |
|o1 : PolynomialRing                                                          |
+-----------------------------------------------------------------------------+
|i2 : J = ideal vars B                                                        |
|                                                                             |
|o2 = ideal (a, b, c, d)                                                      |
|                                                                             |
|o2 : Ideal of B                                                              |
+-----------------------------------------------------------------------------+
|i3 : C = complete res monomialCurveIdeal(B,{1,3,4})                          |
|                                                                             |
|      1      4      4      1                                                 |
|o3 = B  <-- B  <-- B  <-- B  <-- 0                                           |
|                                                                             |
|     0      1      2      3      4                                           |
|                                                                             |
|o3 : ChainComplex                                                            |
+-----------------------------------------------------------------------------+
|i4 : K = filteredComplex(J,C,4)                                              |
|                                                                             |
|o4 = -5 : image 0 <-- image 0 <-- image 0 <-- image 0 <-- image 0            |
|                                                                             |
|          0           1           2           3           4                  |
|                                                                             |
|     -4 : image | a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c      |
|                                                                             |
|          0                                                                  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|     -3 : image | a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3 b2c b2d bc2      |
|                                                                             |
|          0                                                                  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|     -2 : image | a2 ab ac ad b2 bc bd c2 cd d2 | <-- image {2} | a2 0       |
|                                                            {3} | 0  a2      |
|          0                                                 {3} | 0  0       |
|                                                            {3} | 0  0       |
|                                                                             |
|                                                      1                      |
|                                                                             |
|     -1 : image | a b c d | <-- image {2} | a 0 0 0 b 0 0 0 c 0 0 0 d 0      |
|                                      {3} | 0 a 0 0 0 b 0 0 0 c 0 0 0 d      |
|          0                           {3} | 0 0 a 0 0 0 b 0 0 0 c 0 0 0      |
|                                      {3} | 0 0 0 a 0 0 0 b 0 0 0 c 0 0      |
|                                                                             |
|                                1                                            |
|                                                                             |
|          1      4      4      1                                             |
|     0 : B  <-- B  <-- B  <-- B  <-- 0                                       |
|                                                                             |
|         0      1      2      3      4                                       |
|                                                                             |
|o4 : FilteredComplex                                                         |
|-----------------------------------------------------------------------------|
|ab2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d     |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|bcd bd2 c3 c2d cd2 d3 | <-- image {2} | a3 0  0  0  a2b 0   0   0   a2c      |
|                                  {3} | 0  a3 0  0  0   a2b 0   0   0        |
|                                  {3} | 0  0  a3 0  0   0   a2b 0   0        |
|                                  {3} | 0  0  0  a3 0   0   0   a2b 0        |
|                                                                             |
|                            1                                                |
|                                                                             |
|0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0       |
|0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd      |
|a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0       |
|0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0       |
|                                                                             |
|                                                                             |
|                                                                             |
|0 0 | <-- image {4} | a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 | <-- image {5} |      |
|0 0 |           {4} | 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 |                      |
|d 0 |           {4} | 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 |     3                |
|0 d |           {4} | 0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d |                      |
|                                                                             |
|          2                                                                  |
|-----------------------------------------------------------------------------|
| bcd2 bd3 c4 c3d c2d2 cd3 d4 | <-- image {2} | a4 0  0  0  a3b 0   0   0     |
|                                         {3} | 0  a4 0  0  0   a3b 0   0     |
|                                         {3} | 0  0  a4 0  0   0   a3b 0     |
|                                         {3} | 0  0  0  a4 0   0   0   a3b   |
|                                                                             |
|                                   1                                         |
|                                                                             |
|0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0    |
|a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0    |
|0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0    |
|0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd  |
|                                                                             |
|                                                                             |
|                                                                             |
|0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  | <-- image {4} | a2 0  0  0  ab   |
|0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |           {4} | 0  a2 0  0  0    |
|bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |           {4} | 0  0  a2 0  0    |
|0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |           {4} | 0  0  0  a2 0    |
|                                                                             |
|                                                2                            |
|                                                                             |
|a b c d | <-- image 0                                                        |
|                                                                             |
|              4                                                              |
|-----------------------------------------------------------------------------|
|a3c 0   0   0   a3d 0   0   0   a2b2 0    0    0    a2bc 0    0    0    a2bd |
|0   a3c 0   0   0   a3d 0   0   0    a2b2 0    0    0    a2bc 0    0    0    |
|0   0   a3c 0   0   0   a3d 0   0    0    a2b2 0    0    0    a2bc 0    0    |
|0   0   0   a3c 0   0   0   a3d 0    0    0    a2b2 0    0    0    a2bc 0    |
|                                                                             |
|                                                                             |
|                                                                             |
| ac2 0   0   0   acd 0   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   |
| 0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   |
| 0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   |
| 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c |
|                                                                             |
|                                                                             |
|                                                                             |
|0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0 |
|ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0 |
|0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2|
|0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0 |
|-----------------------------------------------------------------------------|
|0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0           |
|a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0           |
|0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2        |
|0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0           |
|                                                                             |
|                                                                             |
|                                                                             |
|b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0   c3 0         |
|0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3        |
|0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0  0         |
|0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0  0         |
|                                                                             |
|                                                                             |
|                                                                             |
| 0  cd 0  0  0  d2 0  0  0  | <-- image {5} | a2 ab ac ad b2 bc bd c2        |
| 0  0  cd 0  0  0  d2 0  0  |                                                |
| 0  0  0  cd 0  0  0  d2 0  |     3                                          |
| c2 0  0  0  cd 0  0  0  d2 |                                                |
|-----------------------------------------------------------------------------|
|0    ab3 0   0   0   ab2c 0    0    0    ab2d 0    0    0    abc2 0          |
|0    0   ab3 0   0   0    ab2c 0    0    0    ab2d 0    0    0    abc2       |
|0    0   0   ab3 0   0    0    ab2c 0    0    0    ab2d 0    0    0          |
|a2d2 0   0   0   ab3 0    0    0    ab2c 0    0    0    ab2d 0    0          |
|                                                                             |
|                                                                             |
|                                                                             |
|0  0  c2d 0   0   0   cd2 0   0   0   d3 0  0  0  | <-- image {4} | a3       |
|0  0  0   c2d 0   0   0   cd2 0   0   0  d3 0  0  |           {4} | 0        |
|c3 0  0   0   c2d 0   0   0   cd2 0   0  0  d3 0  |           {4} | 0        |
|0  c3 0   0   0   c2d 0   0   0   cd2 0  0  0  d3 |           {4} | 0        |
|                                                                             |
|                                                        2                    |
|                                                                             |
|cd d2 | <-- image 0                                                          |
|                                                                             |
|            4                                                                |
|-----------------------------------------------------------------------------|
|0    0    abcd 0    0    0    abd2 0    0                                    |
|0    0    0    abcd 0    0    0    abd2 0                                    |
|abc2 0    0    0    abcd 0    0    0    abd2                                 |
|0    abc2 0    0    0    abcd 0    0    0                                    |
|                                                                             |
|                                                                             |
|                                                                             |
|0  0  0  a2b 0   0   0   a2c 0   0   0   a2d                                 |
|a3 0  0  0   a2b 0   0   0   a2c 0   0   0                                   |
|0  a3 0  0   0   a2b 0   0   0   a2c 0   0                                   |
|0  0  a3 0   0   0   a2b 0   0   0   a2c 0                                   |
|-----------------------------------------------------------------------------|
|0    ac3 0   0   0   ac2d 0    0    0    acd2 0    0                         |
|0    0   ac3 0   0   0    ac2d 0    0    0    acd2 0                         |
|0    0   0   ac3 0   0    0    ac2d 0    0    0    acd2                      |
|abd2 0   0   0   ac3 0    0    0    ac2d 0    0    0                         |
|                                                                             |
|                                                                             |
|                                                                             |
|0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0                        |
|a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0                        |
|0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd                      |
|0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0                        |
|-----------------------------------------------------------------------------|
|0    ad3 0   0   0   b4 0  0  0  b3c 0   0   0   b3d 0   0                   |
|0    0   ad3 0   0   0  b4 0  0  0   b3c 0   0   0   b3d 0                   |
|0    0   0   ad3 0   0  0  b4 0  0   0   b3c 0   0   0   b3d                 |
|acd2 0   0   0   ad3 0  0  0  b4 0   0   0   b3c 0   0   0                   |
|                                                                             |
|                                                                             |
|                                                                             |
|0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0   b3 0  0                  |
|0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0  b3 0                  |
|0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0  0  b3                 |
|abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0  0  0                  |
|-----------------------------------------------------------------------------|
|0   b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0                      |
|0   0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0                      |
|0   0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2                   |
|b3d 0    0    0    b2c2 0    0    0    b2cd 0    0    0                      |
|                                                                             |
|                                                                             |
|                                                                             |
|0  b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0                     |
|0  0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd                   |
|0  0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0                     |
|b3 0   0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0                     |
|-----------------------------------------------------------------------------|
|0    bc3 0   0   0   bc2d 0    0    0    bcd2 0    0    0    bd3 0   0   0   |
|0    0   bc3 0   0   0    bc2d 0    0    0    bcd2 0    0    0   bd3 0   0   |
|0    0   0   bc3 0   0    0    bc2d 0    0    0    bcd2 0    0   0   bd3 0   |
|b2d2 0   0   0   bc3 0    0    0    bc2d 0    0    0    bcd2 0   0   0   bd3 |
|                                                                             |
|                                                                             |
|                                                                             |
|0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0   0   d3 0  0  |
|0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0   0   0  d3 0  |
|bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2 0   0  0  d3 |
|0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0   cd2 0  0  0  |
|-----------------------------------------------------------------------------|
|c4 0  0  0  c3d 0   0   0   c2d2 0    0    0    cd3 0   0   0   d4           |
|0  c4 0  0  0   c3d 0   0   0    c2d2 0    0    0   cd3 0   0   0            |
|0  0  c4 0  0   0   c3d 0   0    0    c2d2 0    0   0   cd3 0   0            |
|0  0  0  c4 0   0   0   c3d 0    0    0    c2d2 0   0   0   cd3 0            |
|                                                                             |
|                                                                             |
|                                                                             |
|0  | <-- image {5} | a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3 b2c           |
|0  |                                                                         |
|0  |     3                                                                   |
|d3 |                                                                         |
|-----------------------------------------------------------------------------|
|0  0  0  | <-- image {4} | a4 0  0  0  a3b 0   0   0   a3c 0   0   0   a3d   |
|d4 0  0  |           {4} | 0  a4 0  0  0   a3b 0   0   0   a3c 0   0   0     |
|0  d4 0  |           {4} | 0  0  a4 0  0   0   a3b 0   0   0   a3c 0   0     |
|0  0  d4 |           {4} | 0  0  0  a4 0   0   0   a3b 0   0   0   a3c 0     |
|                                                                             |
|               2                                                             |
|                                                                             |
|b2d bc2 bcd bd2 c3 c2d cd2 d3 | <-- image 0                                  |
|                                                                             |
|                                    4                                        |
|-----------------------------------------------------------------------------|
|0   0   0   a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    a2c2 |
|a3d 0   0   0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    |
|0   a3d 0   0    0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    |
|0   0   a3d 0    0    0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    |
|-----------------------------------------------------------------------------|
|0    0    0    a2cd 0    0    0    a2d2 0    0    0    ab3 0   0   0   ab2c  |
|a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0    0   ab3 0   0   0     |
|0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0   0   ab3 0   0     |
|0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0   0   0   ab3 0     |
|-----------------------------------------------------------------------------|
|0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0      |
|ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0      |
|0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0      |
|0    0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd   |
|-----------------------------------------------------------------------------|
|abd2 0    0    0    ac3 0   0   0   ac2d 0    0    0    acd2 0    0    0     |
|0    abd2 0    0    0   ac3 0   0   0    ac2d 0    0    0    acd2 0    0     |
|0    0    abd2 0    0   0   ac3 0   0    0    ac2d 0    0    0    acd2 0     |
|0    0    0    abd2 0   0   0   ac3 0    0    0    ac2d 0    0    0    acd2  |
|-----------------------------------------------------------------------------|
|ad3 0   0   0   b4 0  0  0  b3c 0   0   0   b3d 0   0   0   b2c2 0    0      |
|0   ad3 0   0   0  b4 0  0  0   b3c 0   0   0   b3d 0   0   0    b2c2 0      |
|0   0   ad3 0   0  0  b4 0  0   0   b3c 0   0   0   b3d 0   0    0    b2c2   |
|0   0   0   ad3 0  0  0  b4 0   0   0   b3c 0   0   0   b3d 0    0    0      |
|-----------------------------------------------------------------------------|
|0    b2cd 0    0    0    b2d2 0    0    0    bc3 0   0   0   bc2d 0    0     |
|0    0    b2cd 0    0    0    b2d2 0    0    0   bc3 0   0   0    bc2d 0     |
|0    0    0    b2cd 0    0    0    b2d2 0    0   0   bc3 0   0    0    bc2d  |
|b2c2 0    0    0    b2cd 0    0    0    b2d2 0   0   0   bc3 0    0    0     |
|-----------------------------------------------------------------------------|
|0    bcd2 0    0    0    bd3 0   0   0   c4 0  0  0  c3d 0   0   0   c2d2    |
|0    0    bcd2 0    0    0   bd3 0   0   0  c4 0  0  0   c3d 0   0   0       |
|0    0    0    bcd2 0    0   0   bd3 0   0  0  c4 0  0   0   c3d 0   0       |
|bc2d 0    0    0    bcd2 0   0   0   bd3 0  0  0  c4 0   0   0   c3d 0       |
|-----------------------------------------------------------------------------|
|0    0    0    cd3 0   0   0   d4 0  0  0  | <-- image {5} | a4 a3b a3c a3d  |
|c2d2 0    0    0   cd3 0   0   0  d4 0  0  |                                 |
|0    c2d2 0    0   0   cd3 0   0  0  d4 0  |     3                           |
|0    0    c2d2 0   0   0   cd3 0  0  0  d4 |                                 |
|-----------------------------------------------------------------------------|
|a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab2d abc2 abcd abd2 ac3 ac2d acd2 ad3 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 bd3 c4 c3d c2d2 cd3 d4 | <-- image 0 |
|                                                                             |
|                                                                     4       |
+-----------------------------------------------------------------------------+

Here are some higher pages of the associated spectral sequence:

+-----------------------------------------------------------------------------+
|i5 : E = prune spectralSequence K                                            |
|                                                                             |
|o5 = E                                                                       |
|                                                                             |
|o5 : SpectralSequence                                                        |
+-----------------------------------------------------------------------------+
|i6 : E^4                                                                     |
|                                                                             |
|     +-----------------------------------------------------------------------|
|o6 = |cokernel {4} | -d -b 0  -c 0  0  -d -c 0  0  0  0  0  -d 0  0  0  0  0 |
|     |         {4} | c  a  -d 0  -b 0  0  0  0  -d 0  0  -d 0  0  0  0  0  0 |
|     |         {4} | 0  0  c  b  a  -d 0  0  -d 0  0  0  0  0  0  0  -d 0  0 |
|     |         {4} | 0  0  0  0  0  c  b  a  0  0  0  -d 0  0  0  -d 0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  b  a  c  0  0  0  -d 0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  -d c  b  a  0  0  0  0  -d|
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  -d 0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |                                                                       |
|     |{-4, 4}                                                                |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 3}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 2}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 1}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 0}                                                                |
|     +-----------------------------------------------------------------------|
|                                                                             |
|o6 : SpectralSequencePage                                                    |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| a  -d 0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  c  b  a  -d 0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  c  b  a  -d 0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  c  b  a  -d 0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  c  b  a  -d 0  0  0  0  0  0  -d 0  0  0  -d 0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  -d 0  0  0  0  0  0  -d 0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  -d 0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  -d 0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  -|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|---------+-------------------------------------------------------------------|
|  0  0  ||0                                                                  |
|  0  0  ||                                                                   |
|  0  0  ||{-3, 4}                                                            |
|  0  0  ||                                                                   |
|  0  0  ||                                                                   |
|  0  0  ||                                                                   |
|  0  0  ||                                                                   |
|  0  0  ||                                                                   |
|  0  0  ||                                                                   |
|  0  0  ||                                                                   |
|  0  0  ||                                                                   |
|  0  0  ||                                                                   |
|  0  -d ||                                                                   |
|  -d 0  ||                                                                   |
|  0  0  ||                                                                   |
|d 0  0  ||                                                                   |
|  b  a  ||                                                                   |
|         |                                                                   |
|         |                                                                   |
|---------+-------------------------------------------------------------------|
|         |cokernel {3} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|         |         {3} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|         |         {3} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|         |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 |
|         |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 |
|         |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 |
|         |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c |
|         |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|         |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|         |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|         |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|         |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|         |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|         |                                                                   |
|         |{-3, 3}                                                            |
|---------+-------------------------------------------------------------------|
|         |0                                                                  |
|         |                                                                   |
|         |{-3, 2}                                                            |
|         |                                                                   |
|         |                                                                   |
|         |                                                                   |
|         |                                                                   |
|         |                                                                   |
|         |                                                                   |
|         |                                                                   |
|         |                                                                   |
|---------+-------------------------------------------------------------------|
|         |0                                                                  |
|         |                                                                   |
|         |{-3, 1}                                                            |
|         |                                                                   |
|         |                                                                   |
|         |                                                                   |
|---------+-------------------------------------------------------------------|
|         |0                                                                  |
|         |                                                                   |
|         |{-3, 0}                                                            |
|---------+-------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------+-----------------------|
|                                                     |0                      |
|                                                     |                       |
|                                                     |{-2, 4}                |
|                                                     |                       |
|                                                     |                       |
|                                                     |                       |
|                                                     |                       |
|                                                     |                       |
|                                                     |                       |
|                                                     |                       |
|                                                     |                       |
|                                                     |                       |
|                                                     |                       |
|                                                     |                       |
|                                                     |                       |
|                                                     |                       |
|                                                     |                       |
|                                                     |                       |
|                                                     |                       |
|-----------------------------------------------------+-----------------------|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||0                      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                       |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||{-2, 3}                |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                       |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                       |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                       |
|b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                       |
|0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                       |
|0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                       |
|0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 ||                       |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 ||                       |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 ||                       |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a ||                       |
|                                                     |                       |
|                                                     |                       |
|-----------------------------------------------------+-----------------------|
|                                                     |cokernel {2} | d c b a |
|                                                     |         {2} | 0 0 0 0 |
|                                                     |         {2} | 0 0 0 0 |
|                                                     |         {2} | 0 0 0 0 |
|                                                     |         {2} | 0 0 0 0 |
|                                                     |         {2} | 0 0 0 0 |
|                                                     |         {2} | 0 0 0 0 |
|                                                     |         {2} | 0 0 0 0 |
|                                                     |         {2} | 0 0 0 0 |
|                                                     |                       |
|                                                     |{-2, 2}                |
|-----------------------------------------------------+-----------------------|
|                                                     |0                      |
|                                                     |                       |
|                                                     |{-2, 1}                |
|                                                     |                       |
|                                                     |                       |
|                                                     |                       |
|-----------------------------------------------------+-----------------------|
|                                                     |0                      |
|                                                     |                       |
|                                                     |{-2, 0}                |
|-----------------------------------------------------+-----------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------+-----------|
|                                                                 |0          |
|                                                                 |           |
|                                                                 |{-1, 4}    |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|-----------------------------------------------------------------+-----------|
|                                                                 |0          |
|                                                                 |           |
|                                                                 |{-1, 3}    |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|-----------------------------------------------------------------+-----------|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||0          |
|d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||           |
|0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||{-1, 2}    |
|0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||           |
|0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||           |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 ||           |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 ||           |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 ||           |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a ||           |
|                                                                 |           |
|                                                                 |           |
|-----------------------------------------------------------------+-----------|
|                                                                 |cokernel {1|
|                                                                 |         {1|
|                                                                 |         {1|
|                                                                 |         {1|
|                                                                 |           |
|                                                                 |{-1, 1}    |
|-----------------------------------------------------------------+-----------|
|                                                                 |0          |
|                                                                 |           |
|                                                                 |{-1, 0}    |
|-----------------------------------------------------------------+-----------|
|-----------------------------------------------------------------------------|
|-------------------------------------+--------------------+                  |
|                                     |0                   |                  |
|                                     |                    |                  |
|                                     |{0, 4}              |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|-------------------------------------+--------------------+                  |
|                                     |0                   |                  |
|                                     |                    |                  |
|                                     |{0, 3}              |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|-------------------------------------+--------------------+                  |
|                                     |0                   |                  |
|                                     |                    |                  |
|                                     |{0, 2}              |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|-------------------------------------+--------------------+                  |
|} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 ||0                   |                  |
|} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 ||                    |                  |
|} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 ||{0, 1}              |                  |
|} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a ||                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|-------------------------------------+--------------------+                  |
|                                     |cokernel | d c b a ||                  |
|                                     |                    |                  |
|                                     |{0, 0}              |                  |
|-------------------------------------+--------------------+                  |
+-----------------------------------------------------------------------------+
|i7 : E^4 .dd                                                                 |
|                                                                             |
|o7 = {-9, 8} : 0 <----- 0 : {-5, 5}                                          |
|                    0                                                        |
|                                                                             |
|     {-9, 9} : 0 <----- 0 : {-5, 6}                                          |
|                    0                                                        |
|                                                                             |
|     {-9, 10} : 0 <----- 0 : {-5, 7}                                         |
|                     0                                                       |
|                                                                             |
|     {-9, 11} : 0 <----- 0 : {-5, 8}                                         |
|                     0                                                       |
|                                                                             |
|     {-9, 12} : 0 <----- 0 : {-5, 9}                                         |
|                     0                                                       |
|                                                                             |
|     {-4, 3} : 0 <----- cokernel | d c b a | : {0, 0}                        |
|                    0                                                        |
|                                                                             |
|     {-4, 4} : cokernel {4} | -d -b 0  -c 0  0  -d -c 0  0  0  0  0  -d 0    |
|                        {4} | c  a  -d 0  -b 0  0  0  0  -d 0  0  -d 0  0    |
|                        {4} | 0  0  c  b  a  -d 0  0  -d 0  0  0  0  0  0    |
|                        {4} | 0  0  0  0  0  c  b  a  0  0  0  -d 0  0  0    |
|                        {4} | 0  0  0  0  0  0  0  0  b  a  c  0  0  0  -d   |
|                        {4} | 0  0  0  0  0  0  0  0  0  0  -d c  b  a  0    |
|                        {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  c    |
|                        {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0    |
|                        {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0    |
|                        {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0    |
|                        {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0    |
|                        {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0    |
|                        {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0    |
|                        {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0    |
|                        {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0    |
|                        {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0    |
|                        {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0    |
|                                                                             |
|     {-4, 5} : 0 <----- 0 : {0, 2}                                           |
|                    0                                                        |
|                                                                             |
|     {-4, 6} : 0 <----- 0 : {0, 3}                                           |
|                    0                                                        |
|                                                                             |
|     {-4, 7} : 0 <----- 0 : {0, 4}                                           |
|                    0                                                        |
|                                                                             |
|     {-5, 4} : 0 <----- cokernel {1} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 | :   |
|                    0            {1} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 |     |
|                                 {1} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 |     |
|                                 {1} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a |     |
|                                                                             |
|     {-5, 5} : 0 <----- 0 : {-1, 2}                                          |
|                    0                                                        |
|                                                                             |
|     {-5, 6} : 0 <----- 0 : {-1, 3}                                          |
|                    0                                                        |
|                                                                             |
|     {-5, 7} : 0 <----- 0 : {-1, 4}                                          |
|                    0                                                        |
|                                                                             |
|     {-5, 8} : 0 <----- 0 : {-1, 5}                                          |
|                    0                                                        |
|                                                                             |
|     {-6, 5} : 0 <----- cokernel {2} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0   |
|                    0            {2} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0   |
|                                 {2} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0   |
|                                 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0   |
|                                 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c   |
|                                 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0   |
|                                 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0   |
|                                 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0   |
|                                 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0   |
|                                                                             |
|     {-6, 6} : 0 <----- 0 : {-2, 3}                                          |
|                    0                                                        |
|                                                                             |
|     {-6, 7} : 0 <----- 0 : {-2, 4}                                          |
|                    0                                                        |
|                                                                             |
|     {-6, 8} : 0 <----- 0 : {-2, 5}                                          |
|                    0                                                        |
|                                                                             |
|     {-6, 9} : 0 <----- 0 : {-2, 6}                                          |
|                    0                                                        |
|                                                                             |
|     {-7, 6} : 0 <----- cokernel {3} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0   |
|                    0            {3} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0   |
|                                 {3} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0   |
|                                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0   |
|                                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c   |
|                                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0   |
|                                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0   |
|                                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0   |
|                                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0   |
|                                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0   |
|                                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0   |
|                                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0   |
|                                 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0   |
|                                                                             |
|     {-7, 7} : 0 <----- 0 : {-3, 4}                                          |
|                    0                                                        |
|                                                                             |
|     {-7, 8} : 0 <----- 0 : {-3, 5}                                          |
|                    0                                                        |
|                                                                             |
|     {-7, 9} : 0 <----- 0 : {-3, 6}                                          |
|                    0                                                        |
|                                                                             |
|     {-7, 10} : 0 <----- 0 : {-3, 7}                                         |
|                     0                                                       |
|                                                                             |
|     {-8, 7} : 0 <----- cokernel {4} | -d -b 0  -c 0  0  -d -c 0  0  0  0    |
|                    0            {4} | c  a  -d 0  -b 0  0  0  0  -d 0  0    |
|                                 {4} | 0  0  c  b  a  -d 0  0  -d 0  0  0    |
|                                 {4} | 0  0  0  0  0  c  b  a  0  0  0  -d   |
|                                 {4} | 0  0  0  0  0  0  0  0  b  a  c  0    |
|                                 {4} | 0  0  0  0  0  0  0  0  0  0  -d c    |
|                                 {4} | 0  0  0  0  0  0  0  0  0  0  0  0    |
|                                 {4} | 0  0  0  0  0  0  0  0  0  0  0  0    |
|                                 {4} | 0  0  0  0  0  0  0  0  0  0  0  0    |
|                                 {4} | 0  0  0  0  0  0  0  0  0  0  0  0    |
|                                 {4} | 0  0  0  0  0  0  0  0  0  0  0  0    |
|                                 {4} | 0  0  0  0  0  0  0  0  0  0  0  0    |
|                                 {4} | 0  0  0  0  0  0  0  0  0  0  0  0    |
|                                 {4} | 0  0  0  0  0  0  0  0  0  0  0  0    |
|                                 {4} | 0  0  0  0  0  0  0  0  0  0  0  0    |
|                                 {4} | 0  0  0  0  0  0  0  0  0  0  0  0    |
|                                 {4} | 0  0  0  0  0  0  0  0  0  0  0  0    |
|                                                                             |
|     {-8, 8} : 0 <----- 0 : {-4, 5}                                          |
|                    0                                                        |
|                                                                             |
|     {-8, 9} : 0 <----- 0 : {-4, 6}                                          |
|                    0                                                        |
|                                                                             |
|     {-8, 10} : 0 <----- 0 : {-4, 7}                                         |
|                     0                                                       |
|                                                                             |
|     {-8, 11} : 0 <----- 0 : {-4, 8}                                         |
|                     0                                                       |
|                                                                             |
|o7 : SpectralSequencePageMap                                                 |
|-----------------------------------------------------------------------------|
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0       |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0       |
|0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0       |
|-d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0       |
|0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0       |
|0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0       |
|b  a  -d 0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0       |
|0  0  c  b  a  -d 0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0       |
|0  0  0  0  0  c  b  a  -d 0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0       |
|0  0  0  0  0  0  0  0  c  b  a  -d 0  0  0  0  0  0  -d 0  0  0  -d 0       |
|0  0  0  0  0  0  0  0  0  0  0  c  b  a  -d 0  0  0  0  0  0  -d 0  0       |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  -d 0  0  0  0  0  0       |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  -d 0  0  0       |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  -d      |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c       |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0       |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0       |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|{-1, 1}                                                                      |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | : {-2, 2}                              |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                        |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                        |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                        |
|b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                        |
|0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 |                                        |
|0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 |                                        |
|0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 |                                        |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a |                                        |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | :      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |        |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |        |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |        |
|b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |        |
|0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |        |
|0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |        |
|0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |        |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |        |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 |        |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 |        |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 |        |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a |        |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0       |
|-d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0       |
|0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0       |
|0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0       |
|0  0  -d 0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0       |
|b  a  0  0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0       |
|0  0  c  b  a  -d 0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0       |
|0  0  0  0  0  c  b  a  -d 0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0       |
|0  0  0  0  0  0  0  0  c  b  a  -d 0  0  0  0  0  0  -d 0  0  0  -d 0       |
|0  0  0  0  0  0  0  0  0  0  0  c  b  a  -d 0  0  0  0  0  0  -d 0  0       |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  -d 0  0  0  0  0  0       |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  -d 0  0  0       |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  -d      |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c       |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0       |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0       |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0       |
|-----------------------------------------------------------------------------|
|0  0  0  0  0  0  0  0  | <----- 0 : {0, 1}                                  |
|0  0  0  0  0  0  0  0  |    0                                               |
|0  0  0  0  0  0  0  0  |                                                    |
|0  0  0  0  0  0  0  0  |                                                    |
|0  0  0  0  0  0  0  0  |                                                    |
|0  0  0  0  0  0  0  0  |                                                    |
|0  0  0  0  0  0  0  0  |                                                    |
|0  0  0  0  0  0  0  0  |                                                    |
|0  0  0  0  0  0  0  0  |                                                    |
|0  0  0  0  0  0  0  0  |                                                    |
|0  -d 0  0  0  0  0  0  |                                                    |
|-d 0  0  0  -d 0  0  0  |                                                    |
|0  0  0  -d 0  0  0  -d |                                                    |
|0  0  0  0  0  0  -d 0  |                                                    |
|b  a  -d 0  0  0  0  0  |                                                    |
|0  0  c  b  a  -d 0  0  |                                                    |
|0  0  0  0  0  c  b  a  |                                                    |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|{-3, 3}                                                                      |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0  0  0  0  0  0  0  0  0  0  0  | : {-4, 4}                                 |
|0  0  0  0  0  0  0  0  0  0  0  |                                           |
|0  0  0  0  0  0  0  0  0  0  0  |                                           |
|0  0  0  0  0  0  0  0  0  0  0  |                                           |
|0  0  0  0  0  0  0  0  0  0  0  |                                           |
|0  0  0  0  0  0  0  0  0  0  0  |                                           |
|0  0  0  0  0  0  0  0  0  0  0  |                                           |
|0  0  0  0  0  0  0  0  0  0  0  |                                           |
|0  0  0  0  0  0  0  0  0  0  0  |                                           |
|0  -d 0  0  0  0  0  0  0  0  0  |                                           |
|-d 0  0  0  -d 0  0  0  0  0  0  |                                           |
|0  0  0  -d 0  0  0  -d 0  0  0  |                                           |
|0  0  0  0  0  0  -d 0  0  0  -d |                                           |
|b  a  -d 0  0  0  0  0  0  -d 0  |                                           |
|0  0  c  b  a  -d 0  0  0  0  0  |                                           |
|0  0  0  0  0  c  b  a  -d 0  0  |                                           |
|0  0  0  0  0  0  0  0  c  b  a  |                                           |
+-----------------------------------------------------------------------------+
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:1230:0.

Identifying anti-podal points of the two sphere
***********************************************

In this example we compute the spectral sequence arising from the quotient map
$\mathbb{S}^2 \rightarrow \mathbb{R} \mathbb{P}^2$, given by identifying
anti-podal points. This map can be realized by a simplicial map along the lines
of Exercise 27, Section 6.5 of Armstrong's book Basic Topology. In order to
give a combinatorial picture of the quotient map $\mathbb{S}^2 \rightarrow
\mathbb{R} \mathbb{P}^2$, given by identifying anti-podal points, we first make
an appropriate simplicial realization of $\mathbb{S}^2$. Note that we have
added a few barycentric coordinates.

+-----------------------------------------------------------------------------+
|i1 : S = ZZ[v1,v2,v3,v4,v5,v6,v15,v12,v36,v34,v46,v25];                      |
+-----------------------------------------------------------------------------+
|i2 : twoSphere = simplicialComplex {v3*v4*v5, v5*v4*v15, v15*v34*v4,         |
|-----------------------------------------------------------------------------|
|v15*v34*v1, v34*v1*v6, v34*v46*v6, v36*v46*v6, v3*v4*v46, v4*v46*v34,        |
|-----------------------------------------------------------------------------|
|v3*v46*v36, v1*v6*v2, v6*v2*v36, v2*v36*v12,v36*v12*v3, v12*v3*v5,           |
|-----------------------------------------------------------------------------|
|v12*v5*v25, v25*v5*v15, v2*v12*v25, v1*v2*v25, v1*v25*v15};                  |
+-----------------------------------------------------------------------------+

We can check that the homology of the simplicial complex twoSphere agrees with
that of $\mathbb{S}^2$.

+---------------------------------------------------+
|i3 : C = truncate(chainComplex complex twoSphere,1)|
|                                                   |
|                   12       30       20            |
|o3 = image 0 <-- ZZ   <-- ZZ   <-- ZZ              |
|                                                   |
|     -1          0        1        2               |
|                                                   |
|o3 : ChainComplex                                  |
+---------------------------------------------------+
|i4 : prune HH C                                    |
|                                                   |
|o4 = -1 : 0                                        |
|                                                   |
|            1                                      |
|      0 : ZZ                                       |
|                                                   |
|      1 : 0                                        |
|                                                   |
|            1                                      |
|      2 : ZZ                                       |
|                                                   |
|o4 : GradedModule                                  |
+---------------------------------------------------+

We now write down our simplicial complex whose topological realization is
$\mathbb{R} \mathbb{P}^2$.

+-----------------------------------------------------------------------------+
|i5 : R = ZZ[a,b,c,d,e,f];                                                    |
+-----------------------------------------------------------------------------+
|i6 : realProjectivePlane = simplicialComplex {a*b*c, b*c*d, c*d*e, a*e*d,    |
|-----------------------------------------------------------------------------|
|e*b*a, e*f*b, d*f*b, a*f*d, c*f*e,a*f*c};                                    |
+-----------------------------------------------------------------------------+

Again we can check that we've entered a simplicial complex whose homology
agrees with that of the real projective plane.

+-------------------------------------------------------------+
|i7 : B = truncate(chainComplex complex realProjectivePlane,1)|
|                                                             |
|                   6       15       10                       |
|o7 = image 0 <-- ZZ  <-- ZZ   <-- ZZ                         |
|                                                             |
|     -1          0       1        2                          |
|                                                             |
|o7 : ChainComplex                                            |
+-------------------------------------------------------------+
|i8 : prune HH B                                              |
|                                                             |
|o8 = -1 : 0                                                  |
|                                                             |
|            1                                                |
|      0 : ZZ                                                 |
|                                                             |
|      1 : cokernel | 2 |                                     |
|                                                             |
|      2 : 0                                                  |
|                                                             |
|o8 : GradedModule                                            |
+-------------------------------------------------------------+

We now compute the fibers of the anti-podal quotient map $\mathbb{S}^2
\rightarrow  \mathbb{R} \mathbb{P}^2$. The way this works for example is: $a =
v3 ~ v1, b = v6 ~ v5, d = v36 ~ v15, c = v4 ~ v2, e = v34 ~ v12, f = v46 ~ v25$

The fibers over the vertices of $\mathbb{R} \mathbb{P}^2$ are:

+-----------------------------------------------------------------------------+
|i9 : F0twoSphere = simplicialComplex {v1,v3,v5,v6, v4,v2, v36,v15, v34,v12,  |
|                                                                             |
|o9 = simplicialComplex | v25 v46 v34 v36 v12 v15 v6 v5 v4 v3 v2 v1 |         |
|                                                                             |
|o9 : SimplicialComplex                                                       |
|-----------------------------------------------------------------------------|
|v46,v25}                                                                     |
+-----------------------------------------------------------------------------+

The fibers over the edges of $\mathbb{R}\mathbb{P}^2$ are:

+-----------------------------------------------------------------------------+
|i10 : F1twoSphere = simplicialComplex {v3*v4, v1*v2,v3*v5, v1*v6,v4*v5,      |
|                                                                             |
|o10 = simplicialComplex | v12v25 v15v25 v5v25 v2v25 v1v25 v34v46 v36v46      |
|                                                                             |
|o10 : SimplicialComplex                                                      |
|-----------------------------------------------------------------------------|
|v2*v6, v5*v15, v6*v36, v4*v34,                                               |
|                                                                             |
|v6v46 v4v46 v3v46 v15v34 v6v34                                               |
|-----------------------------------------------------------------------------|
|v2*v12, v15*v34, v36*v12, v1*v15, v3*v36, v46*v34, v25*v12, v6*v34,          |
|                                                                             |
|v4v34 v1v34 v12v36 v6v36 v3v36 v2v36 v5v12 v3v12 v2v12 v5v15 v4v15           |
|-----------------------------------------------------------------------------|
| v5*v12, v6*v46, v5*v25, v36*v46, v15*v25, v3*v46, v1*v25, v4*v15, v2*v36,   |
|                                                                             |
|v1v15 v2v6 v1v6 v4v5 v3v5 v3v4 v1v2 |                                        |
|-----------------------------------------------------------------------------|
|v1*v34, v3*v12, v4*v46, v25*v2}                                              |
+-----------------------------------------------------------------------------+

The fibers over the faces is all of $\mathbb{S}^2$.

+-----------------------------------------------------------------------------+
|i11 : F2twoSphere = twoSphere                                                |
|                                                                             |
|o11 = simplicialComplex | v5v12v25 v2v12v25 v5v15v25 v1v15v25 v1v2v25        |
|                                                                             |
|o11 : SimplicialComplex                                                      |
|-----------------------------------------------------------------------------|
|v6v34v46 v4v34v46 v6v36v46 v3v36v46 v3v4v46 v4v15v34 v1v15v34 v1v6v34        |
|-----------------------------------------------------------------------------|
|v3v12v36 v2v12v36 v2v6v36 v3v5v12 v4v5v15 v1v2v6 v3v4v5 |                    |
+-----------------------------------------------------------------------------+

The resulting filtered complex is:

+-----------------------------------------------------------------------------+
|i12 : K = filteredComplex({F2twoSphere, F1twoSphere, F0twoSphere},           |
|                                                                             |
|o12 = -1 : image 0 <-- image 0 <-- image 0 <-- image 0                       |
|                                                                             |
|           -1          0           1           2                             |
|                                                                             |
|      0 : image 0 <-- image | 1 0 0 0 0 0 0 0 0 0 0 0 | <-- image 0          |
|                            | 0 1 0 0 0 0 0 0 0 0 0 0 |                      |
|          -1                | 0 0 1 0 0 0 0 0 0 0 0 0 |     1                |
|                            | 0 0 0 1 0 0 0 0 0 0 0 0 |                      |
|                            | 0 0 0 0 1 0 0 0 0 0 0 0 |                      |
|                            | 0 0 0 0 0 1 0 0 0 0 0 0 |                      |
|                            | 0 0 0 0 0 0 1 0 0 0 0 0 |                      |
|                            | 0 0 0 0 0 0 0 1 0 0 0 0 |                      |
|                            | 0 0 0 0 0 0 0 0 1 0 0 0 |                      |
|                            | 0 0 0 0 0 0 0 0 0 1 0 0 |                      |
|                            | 0 0 0 0 0 0 0 0 0 0 1 0 |                      |
|                            | 0 0 0 0 0 0 0 0 0 0 0 1 |                      |
|                                                                             |
|                      0                                                      |
|                                                                             |
|      1 : image 0 <-- image | 1 0 0 0 0 0 0 0 0 0 0 0 | <-- image |          |
|                            | 0 1 0 0 0 0 0 0 0 0 0 0 |           |          |
|          -1                | 0 0 1 0 0 0 0 0 0 0 0 0 |           |          |
|                            | 0 0 0 1 0 0 0 0 0 0 0 0 |           |          |
|                            | 0 0 0 0 1 0 0 0 0 0 0 0 |           |          |
|                            | 0 0 0 0 0 1 0 0 0 0 0 0 |           |          |
|                            | 0 0 0 0 0 0 1 0 0 0 0 0 |           |          |
|                            | 0 0 0 0 0 0 0 1 0 0 0 0 |           |          |
|                            | 0 0 0 0 0 0 0 0 1 0 0 0 |           |          |
|                            | 0 0 0 0 0 0 0 0 0 1 0 0 |           |          |
|                            | 0 0 0 0 0 0 0 0 0 0 1 0 |           |          |
|                            | 0 0 0 0 0 0 0 0 0 0 0 1 |           |          |
|                                                                  |          |
|                      0                                           |          |
|                                                                  |          |
|                                                                  |          |
|                                                                  |          |
|                                                                  |          |
|                                                                  |          |
|                                                                  |          |
|                                                                  |          |
|                                                                  |          |
|                                                                  |          |
|                                                                  |          |
|                                                                  |          |
|                                                                  |          |
|                                                                  |          |
|                                                                  |          |
|                                                                  |          |
|                                                                  |          |
|                                                                             |
|                                                            1                |
|                                                                             |
|                        12       30       20                                 |
|      2 : image 0 <-- ZZ   <-- ZZ   <-- ZZ                                   |
|                                                                             |
|          -1          0        1        2                                    |
|                                                                             |
|o12 : FilteredComplex                                                        |
|-----------------------------------------------------------------------------|
|ReducedHomology => false)                                                    |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| <-- image 0                                                                 |
|                                                                             |
|     2                                                                       |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | <-- image 0   |
| 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |               |
| 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |     2         |
| 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |               |
| 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |               |
| 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |               |
| 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |               |
| 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |               |
| 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |               |
| 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |               |
| 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |               |
| 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |               |
| 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |               |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |               |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |               |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |               |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |               |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |               |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |               |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 |               |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 |               |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 |               |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 |               |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 |               |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 |               |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 |               |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 |               |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 |               |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 |               |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 |               |
+-----------------------------------------------------------------------------+

We now compute the resulting spectral sequence.

+-----------------------------------------------------------------------------+
|i13 : E = prune spectralSequence K                                           |
|                                                                             |
|o13 = E                                                                      |
|                                                                             |
|o13 : SpectralSequence                                                       |
+-----------------------------------------------------------------------------+
|i14 : E^0                                                                    |
|                                                                             |
|      +------+------+------+                                                 |
|      |  12  |  30  |  20  |                                                 |
|o14 = |ZZ    |ZZ    |ZZ    |                                                 |
|      |      |      |      |                                                 |
|      |{0, 0}|{1, 0}|{2, 0}|                                                 |
|      +------+------+------+                                                 |
|                                                                             |
|o14 : SpectralSequencePage                                                   |
+-----------------------------------------------------------------------------+
|i15 : E^1                                                                    |
|                                                                             |
|      +------+------+------+                                                 |
|      |  12  |  30  |  20  |                                                 |
|o15 = |ZZ    |ZZ    |ZZ    |                                                 |
|      |      |      |      |                                                 |
|      |{0, 0}|{1, 0}|{2, 0}|                                                 |
|      +------+------+------+                                                 |
|                                                                             |
|o15 : SpectralSequencePage                                                   |
+-----------------------------------------------------------------------------+
|i16 : E^0 .dd                                                                |
|                                                                             |
|o16 = {-1, 0} : 0 <----- 0 : {-1, 1}                                         |
|                     0                                                       |
|                                                                             |
|      {-1, 1} : 0 <----- 0 : {-1, 2}                                         |
|                     0                                                       |
|                                                                             |
|      {-1, 2} : 0 <----- 0 : {-1, 3}                                         |
|                     0                                                       |
|                                                                             |
|      {2, -4} : 0 <----- 0 : {2, -3}                                         |
|                     0                                                       |
|                                                                             |
|      {2, -3} : 0 <----- 0 : {2, -2}                                         |
|                     0                                                       |
|                                                                             |
|      {2, -2} : 0 <----- 0 : {2, -1}                                         |
|                     0                                                       |
|                                                                             |
|                           20                                                |
|      {2, -1} : 0 <----- ZZ   : {2, 0}                                       |
|                     0                                                       |
|                                                                             |
|      {1, -3} : 0 <----- 0 : {1, -2}                                         |
|                     0                                                       |
|                                                                             |
|      {1, -2} : 0 <----- 0 : {1, -1}                                         |
|                     0                                                       |
|                                                                             |
|                           30                                                |
|      {1, -1} : 0 <----- ZZ   : {1, 0}                                       |
|                     0                                                       |
|                                                                             |
|                 30                                                          |
|      {1, 0} : ZZ   <----- 0 : {1, 1}                                        |
|                       0                                                     |
|                                                                             |
|      {0, -2} : 0 <----- 0 : {0, -1}                                         |
|                     0                                                       |
|                                                                             |
|                           12                                                |
|      {0, -1} : 0 <----- ZZ   : {0, 0}                                       |
|                     0                                                       |
|                                                                             |
|                 12                                                          |
|      {0, 0} : ZZ   <----- 0 : {0, 1}                                        |
|                       0                                                     |
|                                                                             |
|      {0, 1} : 0 <----- 0 : {0, 2}                                           |
|                    0                                                        |
|                                                                             |
|      {-1, -1} : 0 <----- 0 : {-1, 0}                                        |
|                      0                                                      |
|                                                                             |
|o16 : SpectralSequencePageMap                                                |
+-----------------------------------------------------------------------------+
|i17 : E^1 .dd                                                                |
|                                                                             |
|o17 = {-2, 1} : 0 <----- 0 : {-1, 1}                                         |
|                     0                                                       |
|                                                                             |
|      {-2, 2} : 0 <----- 0 : {-1, 2}                                         |
|                     0                                                       |
|                                                                             |
|      {-2, 3} : 0 <----- 0 : {-1, 3}                                         |
|                     0                                                       |
|                                                                             |
|      {1, -3} : 0 <----- 0 : {2, -3}                                         |
|                     0                                                       |
|                                                                             |
|      {1, -2} : 0 <----- 0 : {2, -2}                                         |
|                     0                                                       |
|                                                                             |
|      {1, -1} : 0 <----- 0 : {2, -1}                                         |
|                     0                                                       |
|                                                                             |
|                 30                                                          |
|      {1, 0} : ZZ   <--------------------------------------------------------|
|                       | -1 -1 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 1  0  -1 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  -1 -1 0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  1  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  1  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | -1 0  0  0  0  -1 0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  -1 -1 0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  1  1  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  -1 0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  -1 -1 0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  1  0  -1 0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  1  -1 0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  1  -1 0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  1  0  0  1  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  -1 0  0  0  0  -1 0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  1  -1 0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  -1 0  0|
|                       | 0  0  0  0  0  0  0  0  0  -1 0  0  0  0  0  1  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  -1 0  0  -1 0|
|                       | 0  0  0  0  0  0  0  0  0  0  -1 0  0  0  0  0  0  -|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  1|
|                       | 0  0  0  0  0  -1 0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  -1 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  -1 0  0  0  0  0  0  0  0  0  0  -1 0  0  0|
|                       | 0  0  0  0  -1 0  0  0  0  0  0  0  0  0  0  0  -1 0|
|                       | 0  0  0  0  0  0  -1 0  0  0  0  -1 0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  -1 0  0  0  0  0  0  0  0  0  -|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  -1 0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -1 0  0|
|                                                                             |
|      {0, -2} : 0 <----- 0 : {1, -2}                                         |
|                     0                                                       |
|                                                                             |
|      {0, -1} : 0 <----- 0 : {1, -1}                                         |
|                     0                                                       |
|                                                                             |
|                 12                                                          |
|      {0, 0} : ZZ   <--------------------------------------------------------|
|                       | 1  1  1  1  1  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | -1 0  0  0  0  1  1  1  1  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  1  1  1  1  1  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  -1 0  0  0  0  1  1  1  1|
|                       | 0  0  0  0  0  0  0  0  0  0  -1 0  0  0  -1 0  0  0|
|                       | 0  -1 0  0  0  -1 0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  -1 0  0  0  0  0  0  0  0  0  0  0  0  -1 0  0|
|                       | 0  0  0  0  0  0  -1 0  0  0  0  -1 0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  -1 0  0  0  0  -1 0  0  0  0  0|
|                       | 0  0  0  -1 0  0  0  0  0  0  0  0  0  0  0  0  -1 0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  -1 0  0  0  -|
|                       | 0  0  0  0  -1 0  0  0  -1 0  0  0  0  0  0  0  0  0|
|                                                                             |
|      {0, 1} : 0 <----- 0 : {1, 1}                                           |
|                    0                                                        |
|                                                                             |
|      {-1, -1} : 0 <----- 0 : {0, -1}                                        |
|                      0                                                      |
|                                                                             |
|                           12                                                |
|      {-1, 0} : 0 <----- ZZ   : {0, 0}                                       |
|                     0                                                       |
|                                                                             |
|      {-1, 1} : 0 <----- 0 : {0, 1}                                          |
|                     0                                                       |
|                                                                             |
|      {-1, 2} : 0 <----- 0 : {0, 2}                                          |
|                     0                                                       |
|                                                                             |
|      {-2, 0} : 0 <----- 0 : {-1, 0}                                         |
|                     0                                                       |
|                                                                             |
|o17 : SpectralSequencePageMap                                                |
|-----------------------------------------------------------------------------|
|              20                                                             |
|----------- ZZ   : {2, 0}                                                    |
|  0  0  |                                                                    |
|  0  0  |                                                                    |
|  0  0  |                                                                    |
|  0  0  |                                                                    |
|  0  0  |                                                                    |
|  0  0  |                                                                    |
|  0  0  |                                                                    |
|  0  0  |                                                                    |
|  0  0  |                                                                    |
|  0  0  |                                                                    |
|  0  0  |                                                                    |
|  0  0  |                                                                    |
|  0  0  |                                                                    |
|  0  0  |                                                                    |
|  0  0  |                                                                    |
|  0  0  |                                                                    |
|  0  0  |                                                                    |
|  0  0  |                                                                    |
|  0  0  |                                                                    |
|1 0  0  |                                                                    |
|  0  0  |                                                                    |
|  -1 0  |                                                                    |
|  0  -1 |                                                                    |
|  1  1  |                                                                    |
|  0  0  |                                                                    |
|  0  0  |                                                                    |
|  0  0  |                                                                    |
|1 0  0  |                                                                    |
|  -1 0  |                                                                    |
|  0  -1 |                                                                    |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                            30                               |
|----------------------------------------- ZZ   : {1, 0}                      |
|  0  0  0  0  0  0  0  0  0  0  0  0  |                                      |
|  0  0  0  0  0  0  0  0  0  0  0  0  |                                      |
|  0  0  0  0  0  0  0  0  0  0  0  0  |                                      |
|  0  0  0  0  0  0  0  0  0  0  0  0  |                                      |
|  1  1  1  0  0  0  0  0  0  0  0  0  |                                      |
|  0  0  0  1  1  1  0  0  0  0  0  0  |                                      |
|  -1 0  0  0  0  0  1  1  0  0  0  0  |                                      |
|  0  -1 0  0  0  0  0  0  1  1  0  0  |                                      |
|  0  0  0  -1 0  0  0  0  -1 0  1  0  |                                      |
|  0  0  0  0  -1 0  -1 0  0  0  0  1  |                                      |
|1 0  0  0  0  0  -1 0  0  0  0  -1 -1 |                                      |
|  0  0  -1 0  0  0  0  -1 0  -1 0  0  |                                      |
+-----------------------------------------------------------------------------+
|i18 : E^2                                                                    |
|                                                                             |
|      +------+------+------+                                                 |
|      |  1   |      |  1   |                                                 |
|o18 = |ZZ    |0     |ZZ    |                                                 |
|      |      |      |      |                                                 |
|      |{0, 0}|{1, 0}|{2, 0}|                                                 |
|      +------+------+------+                                                 |
|                                                                             |
|o18 : SpectralSequencePage                                                   |
+-----------------------------------------------------------------------------+
|i19 : E^2 .dd                                                                |
|                                                                             |
|o19 = {-3, 2} : 0 <----- 0 : {-1, 1}                                         |
|                     0                                                       |
|                                                                             |
|      {-3, 3} : 0 <----- 0 : {-1, 2}                                         |
|                     0                                                       |
|                                                                             |
|      {-3, 4} : 0 <----- 0 : {-1, 3}                                         |
|                     0                                                       |
|                                                                             |
|      {0, -2} : 0 <----- 0 : {2, -3}                                         |
|                     0                                                       |
|                                                                             |
|      {0, -1} : 0 <----- 0 : {2, -2}                                         |
|                     0                                                       |
|                                                                             |
|                 1                                                           |
|      {0, 0} : ZZ  <----- 0 : {2, -1}                                        |
|                      0                                                      |
|                                                                             |
|                          1                                                  |
|      {0, 1} : 0 <----- ZZ  : {2, 0}                                         |
|                    0                                                        |
|                                                                             |
|      {-1, -1} : 0 <----- 0 : {1, -2}                                        |
|                      0                                                      |
|                                                                             |
|      {-1, 0} : 0 <----- 0 : {1, -1}                                         |
|                     0                                                       |
|                                                                             |
|      {-1, 1} : 0 <----- 0 : {1, 0}                                          |
|                     0                                                       |
|                                                                             |
|      {-1, 2} : 0 <----- 0 : {1, 1}                                          |
|                     0                                                       |
|                                                                             |
|      {-2, 0} : 0 <----- 0 : {0, -1}                                         |
|                     0                                                       |
|                                                                             |
|                           1                                                 |
|      {-2, 1} : 0 <----- ZZ  : {0, 0}                                        |
|                     0                                                       |
|                                                                             |
|      {-2, 2} : 0 <----- 0 : {0, 1}                                          |
|                     0                                                       |
|                                                                             |
|      {-2, 3} : 0 <----- 0 : {0, 2}                                          |
|                     0                                                       |
|                                                                             |
|      {-3, 1} : 0 <----- 0 : {-1, 0}                                         |
|                     0                                                       |
|                                                                             |
|o19 : SpectralSequencePageMap                                                |
+-----------------------------------------------------------------------------+
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:1616:0.

inducedMap(FilteredComplex,ZZ) -- the i th inclusion map in a filtered complex
******************************************************************************

  * Function: inducedMap (Macaulay2Doc),
  * Usage:
        f = inducedMap(K,i)
  * Inputs:
      * K, a filtered chain complex,
      * i, an integer (Macaulay2Doc),
  * Optional inputs (Macaulay2Doc),:
      * Degree (Macaulay2Doc),
        => ..., default value null,
      * Verify (Macaulay2Doc),
        => ..., default value true,
  * Outputs:
      * f, a chain complex map (OldChainComplexes),

Description
===========

Returns the chain complex map specifying the inclusion of the i piece of the
filtered complex to the ambient chain complex.

+------------------------------------------------------+
|i1 : A = QQ[x,y];                                     |
+------------------------------------------------------+
|i2 : C = koszul vars A;                               |
+------------------------------------------------------+
|i3 : K = filteredComplex C                            |
|                                                      |
|o3 = -1 : image 0 <-- image 0 <-- image 0             |
|                                                      |
|          0           1           2                   |
|                                                      |
|     0 : image | 1 | <-- image 0 <-- image 0          |
|                                                      |
|         0               1           2                |
|                                                      |
|     1 : image | 1 | <-- image {1} | 1 0 | <-- image 0|
|                               {1} | 0 1 |            |
|         0                                     2      |
|                         1                            |
|                                                      |
|          1      2      1                             |
|     2 : A  <-- A  <-- A                              |
|                                                      |
|         0      1      2                              |
|                                                      |
|o3 : FilteredComplex                                  |
+------------------------------------------------------+
|i4 : inducedMap(K,1)                                  |
|                                                      |
|          1                                           |
|o4 = 0 : A  <--------- image | 1 | : 0                |
|               | 1 |                                  |
|                                                      |
|          2                                           |
|     1 : A  <--------------- image {1} | 1 0 | : 1    |
|               {1} | 1 0 |         {1} | 0 1 |        |
|               {1} | 0 1 |                            |
|                                                      |
|          1                                           |
|     2 : A  <----- image 0 : 2                        |
|               0                                      |
|                                                      |
|o4 : ChainComplexMap                                  |
+------------------------------------------------------+

Ways to use this method:
========================

  * inducedMap(FilteredComplex,ZZ),
    -- the i th inclusion map in a filtered complex
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:3640:0.

max(FilteredComplex) -- maximum spot where the given filtered complex has a module.
***********************************************************************************

  * Function: max (Macaulay2Doc),
  * Usage:
        m = max L
  * Inputs:
      * L, a filtered chain complex,
  * Outputs:
      * m, an integer (Macaulay2Doc),

Description
===========

Returns the maximum spot where the given filtered complex has a module.

Ways to use this method:
========================

  * max(FilteredComplex) -- maximum spot where
    the given filtered complex has a module.
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2656:0.

min(FilteredComplex) -- minimum spot where the given filtered complex has a module.
***********************************************************************************

  * Function: min (Macaulay2Doc),
  * Usage:
        m = min L
  * Inputs:
      * L, a filtered chain complex,
  * Outputs:
      * m, an integer (Macaulay2Doc),

Description
===========

Returns the minimum spot where the given filtered complex has a module.

Ways to use this method:
========================

  * min(FilteredComplex) -- minimum spot where
    the given filtered complex has a module.
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2676:0.

minimalPresentation(SpectralSequence) -- a minimal presentation of a spectral sequence
**************************************************************************************

  * Function: minimalPresentation (Macaulay2Doc),
  * Usage:
        E = minimalPresentation e
  * Inputs:
      * e, a spectral sequence,
  * Optional inputs (Macaulay2Doc),:
      * Exclude (Macaulay2Doc), => ...,
        default value {},
  * Outputs:
      * E, a spectral sequence,

Description
===========

Returns the minimal presentation of a spectral sequence.

If we fail to prune a spectral sequence then the out-put can be highly
unintelligible.

As a specific example consider the filtered complex $K$ below, obtained by
multiplying the minimal free resolution of the rational quartic space curve by
successive powers of the irrelevant ideal.

+----------------------------------------------------+
|i1 : B = QQ[a..d];                                  |
+----------------------------------------------------+
|i2 : J = ideal vars B;                              |
|                                                    |
|o2 : Ideal of B                                     |
+----------------------------------------------------+
|i3 : C = complete res monomialCurveIdeal(B,{1,3,4});|
+----------------------------------------------------+
|i4 : K = filteredComplex(J,C,4);                    |
+----------------------------------------------------+

Compare some pages of the non-pruned version of the spectral sequence with that
of the pruned version.

+-----------------------------------------------------------------------------+
|i5 : E = prune spectralSequence K;                                           |
+-----------------------------------------------------------------------------+
|i6 : e = spectralSequence K;                                                 |
+-----------------------------------------------------------------------------+
|i7 : e^3                                                                     |
|                                                                             |
|     +-----------------------------------------------------------------------|
|o7 = |subquotient (| a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab|
|     |                                                                       |
|     |{-4, 4}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 3}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 2}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 1}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 0}                                                                |
|     +-----------------------------------------------------------------------|
|                                                                             |
|o7 : SpectralSequencePage                                                    |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d3 c4 c3d c2d2 cd3 d4 a2bc-a3d a2b3-a4c a3c2-a2b2d a2c3-a2bd2 ab2c-a2bd ab4-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|3bc a2bc2-ab3d abc3-ab2d2 abc2-a2cd ab3c-a3c2 a2c3-ab2cd ac4-abcd2 abcd-a2d2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|ab3d-a3cd a2c2d-ab2d2 ac3d-abd3 b3c-ab2d b5-a2b2c ab2c2-b4d b2c3-b3d2 b2c2-ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|cd b4c-a2bc2 abc3-b3cd bc4-b2cd2 b2cd-abd2 b4d-a2bcd abc2d-b3d2 bc3d-b2d3 bc3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-ac2d b3c2-a2c3 ac4-b2c2d c5-bc2d2 bc2d-acd2 b3cd-a2c2d ac3d-b2cd2 c4d-bcd3 b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|cd2-ad3 b3d2-a2cd2 ac2d2-b2d3 c3d2-bd4 0 |, | a2bc-a3d a2b3-a4c a3c2-a2b2d a2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c3-a2bd2 ab2c-a2bd ab4-a3bc a2bc2-ab3d abc3-ab2d2 abc2-a2cd ab3c-a3c2 a2c3-ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2cd ac4-abcd2 abcd-a2d2 ab3d-a3cd a2c2d-ab2d2 ac3d-abd3 b3c-ab2d b5-a2b2c ab2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c2-b4d b2c3-b3d2 b2c2-abcd b4c-a2bc2 abc3-b3cd bc4-b2cd2 b2cd-abd2 b4d-a2bcd |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|abc2d-b3d2 bc3d-b2d3 bc3-ac2d b3c2-a2c3 ac4-b2c2d c5-bc2d2 bc2d-acd2 b3cd-a2c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-------------------------------------------------------------------+---------|
|2d ac3d-b2cd2 c4d-bcd3 bcd2-ad3 b3d2-a2cd2 ac2d2-b2d3 c3d2-bd4 0 |)|subquotie|
|                                                                   |         |
|                                                                   |         |
|                                                                   |         |
|                                                                   |         |
|                                                                   |{-3, 4}  |
|-------------------------------------------------------------------+---------|
|                                                                   |subquotie|
|                                                                   |         |
|                                                                   |{-3, 3}  |
|                                                                   |         |
|                                                                   |         |
|                                                                   |         |
|-------------------------------------------------------------------+---------|
|                                                                   |0        |
|                                                                   |         |
|                                                                   |{-3, 2}  |
|                                                                   |         |
|                                                                   |         |
|                                                                   |         |
|-------------------------------------------------------------------+---------|
|                                                                   |0        |
|                                                                   |         |
|                                                                   |{-3, 1}  |
|                                                                   |         |
|                                                                   |         |
|                                                                   |         |
|-------------------------------------------------------------------+---------|
|                                                                   |0        |
|                                                                   |         |
|                                                                   |{-3, 0}  |
|-------------------------------------------------------------------+---------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|nt ({2} | 0 a2b2 a2bd a2bd 0 a3c  a3c  a2c2 a2b2 ab3  ab2d ab2d a2bd a2bc a2b|
|    {3} | 0 -a2c 0    0    0 -a2d -a2d 0    -a2c -abc 0    0    0    -abd -ab|
|    {3} | 0 -a3  a2c  a2c  0 -a2b -a2b a2d  -a3  -a2b abc  abc  a2c  -ab2 -ab|
|    {3} | 0 0    -a3  -a3  0 0    0    -a2b 0    0    -a2b -a2b -a3  0    0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|nt (| a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3 b2c b2d bc2 bcd bd2 c3 c2d cd|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c a2bc abc2 abc2 a2c2 ab2c ab2c abcd abcd abcd 0       abd2 ac3  abd2 0 a2cd |
|d -abd 0    0    0    -ac2 -ac2 0    0    0    acd     0    0    0    0 -ad2 |
|2 -ab2 abd  abd  a2d  -a2c -a2c ac2  ac2  ac2  abc+a2d acd  acd  acd  0 -abd |
|  0    -ab2 -ab2 -a2b 0    0    -a2c -a2c -a2c -a2b    -a2d -abc -a2d 0 0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2 d3 abc-a2d ab3-a3c a2c2-ab2d ac3-abd2 b2c-abd b4-a2bc abc2-b3d bc3-b2d2 bc2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|a2cd a2cd ac2d ac2d ab3  ab2c b4   b3d  b3d  ab2d 0        b2c2 b2c2 abc2 b3c|
|-ad2 -ad2 0    0    -abc -ac2 -b2c 0    0    0    -ac2+b2d 0    0    0    -bc|
|-abd -abd ad2  ad2  -a2b -a2c -ab2 b2c  b2c  abc  b3-a2c   b2d  b2d  abd  -ab|
|0    0    -abd -abd 0    0    0    -ab2 -ab2 -a2b 0        -b3  -b3  -ab2 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-acd b3c-a2c2 ac3-b2cd c4-bcd2 bcd-ad2 b3d-a2cd ac2d-b2d2 c3d-bd3 a4 a3b a3c |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  b3c  b2cd b2cd b2cd abcd 0       b2d2 bc3  b2d2 abd2 0       bc2d bc2d bc3 |
|2 -bc2 0    0    0    0    bcd     0    0    0    0    bd2     0    0    0   |
|c -abc bc2  bc2  bc2  ac2  b2c+abd bcd  bcd  bcd  acd  ac2+b2d bd2  bd2  bcd |
|  0    -abc -abc -abc -a2c -ab2    -abd -b2c -abd -a2d -a2c    -b2d -b2d -b2c|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab2d abc2 abcd abd2 ac3 ac2d acd2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| ac3  0       0        bc2d ac2d 0       bcd2 bcd2 c4   bcd2 0       bd3  c3d|
| 0    c3      0        0    0    c2d     0    0    0    0    cd2     0    0  |
| acd  ac2+b2d c3-bd2   bd2  ad2  bc2+acd c2d  c2d  c2d  c2d  bcd+ad2 cd2  cd2|
| -abc -b3     -ac2+b2d -b2d -abd -abc    -acd -acd -bc2 -acd -abd    -ad2 -bc|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 bd3 c4 c3d c2d2 cd3 d4 |, | abc-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  c3d  0 bd3  0 acd2 acd2 acd2 c2d2 c2d2 0 0 0         0         0 0 0 0 0 0 |
|  0    0 0    0 -d3  -d3  -d3  0    0    0 0 -a2cd     -a2cd     0 0 0 0 0 0 |
|  cd2  0 cd2  0 -bd2 -bd2 -bd2 d3   d3   0 0 -a2bc-a3d -a2bc-a3d 0 0 0 0 0 0 |
|d -bcd 0 -ad2 0 0    0    0    -bd2 -bd2 0 0 a3b       a3b       0 0 0 0 0 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2d ab3-a3c a2c2-ab2d ac3-abd2 b2c-abd b4-a2bc abc2-b3d bc3-b2d2 bc2-acd b3c-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0 0 0 0 0 0 0 0          0 0          0          0 0 0 0 0 0 0         0 0 0 |
|0 0 0 0 0 0 0 -a2c2+ab2d 0 -abcd      -abcd      0 0 0 0 0 0 -ac3+abd2 0 0 0 |
|0 0 0 0 0 0 0 ab3-a3c    0 -ab2c-a2bd -ab2c-a2bd 0 0 0 0 0 0 0         0 0 0 |
|0 0 0 0 0 0 0 0          0 a2b2       a2b2       0 0 0 0 0 0 ab3-a3c   0 0 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2c2 ac3-b2cd c4-bcd2 bcd-ad2 b3d-a2cd ac2d-b2d2 c3d-bd3 a4 a3b a3c a3d a2b2 a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0 0 0 0 0 0 0         0          0         0              0 0 0 0 0 0        |
|0 0 0 0 0 0 -abc2+b3d -a2c2+ab2d -ac3+abd2 -ac3+b2cd+abd2 0 0 0 0 0 -bc3+ac2d|
|0 0 0 0 0 0 b4-a2bc   ab3-a3c    0         b3c+ab2d       0 0 0 0 0 -b3d+a2cd|
|0 0 0 0 0 0 0         0          ab3-a3c   -a3c           0 0 0 0 0 b4-a2bc  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -ab2 -a2c -abd -ac2 -b3 -abc -b2d -bc2 -b2c -ac2|
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ac   ad   0    0    bc  bd   0    0    c2   cd  |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a2   ab   -ac  -ad  ab  b2   -bc  -bd  ac   bc  |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0    0    a2   ab   0   0    ab   b2   0    0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 bd3 c4 c3d c2d2 cd3 d4 |)                  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| -bcd -c3 -b2d -acd -bd2 -c2d a4 0  0  0  a3b 0   0   0   a3c 0   0   0   a3d|
| 0    0   cd   d2   0    0    0  a4 0  0  0   a3b 0   0   0   a3c 0   0   0  |
| -c2  -cd ad   bd   -cd  -d2  0  0  a4 0  0   0   a3b 0   0   0   a3c 0   0  |
| ac   bc  0    0    ad   bd   0  0  0  a4 0   0   0   a3b 0   0   0   a3c 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   0   0   a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    a2c2|
| a3d 0   0   0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0   |
| 0   a3d 0   0    0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0   |
| 0   0   a3d 0    0    0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0    0    0    a2cd 0    0    0    a2d2 0    0    0    ab3 0   0   0   ab2c |
| a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0    0   ab3 0   0   0    |
| 0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0   0   ab3 0   0    |
| 0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0   0   0   ab3 0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0    ab|
|ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0 |
|0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0 |
|0    0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d2 0    0    0    ac3 0   0   0   ac2d 0    0    0    acd2 0    0    0    ad3|
|   abd2 0    0    0   ac3 0   0   0    ac2d 0    0    0    acd2 0    0    0  |
|   0    abd2 0    0   0   ac3 0   0    0    ac2d 0    0    0    acd2 0    0  |
|   0    0    abd2 0   0   0   ac3 0    0    0    ac2d 0    0    0    acd2 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   0   0   b4 0  0  0  b3c 0   0   0   b3d 0   0   0   b2c2 0    0    0    |
| ad3 0   0   0  b4 0  0  0   b3c 0   0   0   b3d 0   0   0    b2c2 0    0    |
| 0   ad3 0   0  0  b4 0  0   0   b3c 0   0   0   b3d 0   0    0    b2c2 0    |
| 0   0   ad3 0  0  0  b4 0   0   0   b3c 0   0   0   b3d 0    0    0    b2c2 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|b2cd 0    0    0    b2d2 0    0    0    bc3 0   0   0   bc2d 0    0    0    b|
|0    b2cd 0    0    0    b2d2 0    0    0   bc3 0   0   0    bc2d 0    0    0|
|0    0    b2cd 0    0    0    b2d2 0    0   0   bc3 0   0    0    bc2d 0    0|
|0    0    0    b2cd 0    0    0    b2d2 0   0   0   bc3 0    0    0    bc2d 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|cd2 0    0    0    bd3 0   0   0   c4 0  0  0  c3d 0   0   0   c2d2 0    0   |
|    bcd2 0    0    0   bd3 0   0   0  c4 0  0  0   c3d 0   0   0    c2d2 0   |
|    0    bcd2 0    0   0   bd3 0   0  0  c4 0  0   0   c3d 0   0    0    c2d2|
|    0    0    bcd2 0   0   0   bd3 0  0  0  c4 0   0   0   c3d 0    0    0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0    cd3 0   0   0   d4 0  0  0  |, {2} | -ab2 -a2c -abd -ac2 -b3 -abc -b2d |
| 0    0   cd3 0   0   0  d4 0  0  |  {3} | ac   ad   0    0    bc  bd   0    |
| 0    0   0   cd3 0   0  0  d4 0  |  {3} | a2   ab   -ac  -ad  ab  b2   -bc  |
| c2d2 0   0   0   cd3 0  0  0  d4 |  {3} | 0    0    a2   ab   0   0    ab   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-bc2 -b2c -ac2 -bcd -c3 -b2d -acd -bd2 -c2d a4 0  0  0  a3b 0   0   0   a3c 0|
|0    c2   cd   0    0   cd   d2   0    0    0  a4 0  0  0   a3b 0   0   0   a|
|-bd  ac   bc   -c2  -cd ad   bd   -cd  -d2  0  0  a4 0  0   0   a3b 0   0   0|
|b2   0    0    ac   bc  0    0    ad   bd   0  0  0  a4 0   0   0   a3b 0   0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|   0   0   a3d 0   0   0   a2b2 0    0    0    a2bc 0    0    0    a2bd 0    |
|3c 0   0   0   a3d 0   0   0    a2b2 0    0    0    a2bc 0    0    0    a2bd |
|   a3c 0   0   0   a3d 0   0    0    a2b2 0    0    0    a2bc 0    0    0    |
|   0   a3c 0   0   0   a3d 0    0    0    a2b2 0    0    0    a2bc 0    0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0    0    ab3 0  |
|0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0    0   ab3|
|a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0   0  |
|0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0   0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   0   ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0  |
| 0   0   0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abc|
| ab3 0   0    0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0  |
| 0   ab3 0    0    0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  0    0    abd2 0    0    0    ac3 0   0   0   ac2d 0    0    0    acd2 0   |
|d 0    0    0    abd2 0    0    0   ac3 0   0   0    ac2d 0    0    0    acd2|
|  abcd 0    0    0    abd2 0    0   0   ac3 0   0    0    ac2d 0    0    0   |
|  0    abcd 0    0    0    abd2 0   0   0   ac3 0    0    0    ac2d 0    0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0    0    ad3 0   0   0   b4 0  0  0  b3c 0   0   0   b3d 0   0   0   b2c2 0|
| 0    0    0   ad3 0   0   0  b4 0  0  0   b3c 0   0   0   b3d 0   0   0    b|
| acd2 0    0   0   ad3 0   0  0  b4 0  0   0   b3c 0   0   0   b3d 0   0    0|
| 0    acd2 0   0   0   ad3 0  0  0  b4 0   0   0   b3c 0   0   0   b3d 0    0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|    0    0    b2cd 0    0    0    b2d2 0    0    0    bc3 0   0   0   bc2d 0 |
|2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0   bc3 0   0   0    bc|
|    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0   0   bc3 0   0    0 |
|    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0   0   0   bc3 0    0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|   0    0    bcd2 0    0    0    bd3 0   0   0   c4 0  0  0  c3d 0   0   0   |
|2d 0    0    0    bcd2 0    0    0   bd3 0   0   0  c4 0  0  0   c3d 0   0   |
|   bc2d 0    0    0    bcd2 0    0   0   bd3 0   0  0  c4 0  0   0   c3d 0   |
|   0    bc2d 0    0    0    bcd2 0   0   0   bd3 0  0  0  c4 0   0   0   c3d |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|--------------------------------------------------+--------------------------|
|c2d2 0    0    0    cd3 0   0   0   d4 0  0  0  |)|subquotient ({4} | ad  bd |
|0    c2d2 0    0    0   cd3 0   0   0  d4 0  0  | |             {4} | -ac -bc|
|0    0    c2d2 0    0   0   cd3 0   0  0  d4 0  | |             {4} | -ab -b2|
|0    0    0    c2d2 0   0   0   cd3 0  0  0  d4 | |             {4} | a2  ab |
|                                                  |                          |
|                                                  |{-2, 4}                   |
|--------------------------------------------------+--------------------------|
|                                                  |subquotient ({2} | 0 ab2 a|
|                                                  |             {3} | 0 -ac 0|
|                                                  |             {3} | 0 -a2 a|
|                                                  |             {3} | 0 0   -|
|                                                  |                          |
|                                                  |{-2, 3}                   |
|--------------------------------------------------+--------------------------|
|                                                  |subquotient (| a2 ab ac ad|
|                                                  |                          |
|                                                  |{-2, 2}                   |
|                                                  |                          |
|                                                  |                          |
|                                                  |                          |
|--------------------------------------------------+--------------------------|
|                                                  |0                         |
|                                                  |                          |
|                                                  |{-2, 1}                   |
|                                                  |                          |
|                                                  |                          |
|                                                  |                          |
|--------------------------------------------------+--------------------------|
|                                                  |0                         |
|                                                  |                          |
|                                                  |{-2, 0}                   |
|--------------------------------------------------+--------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| cd  d2  a2d  0 0 -abd 0 0 0 0 -acd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -b2d -a|
| -c2 -cd -a2c 0 0 abc  0 0 0 0 ac2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b2c  ab|
| -bc -bd -a2b 0 0 ab2  0 0 0 0 abc  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b3   ab|
| ac  ad  a3   0 0 -a2b 0 0 0 0 -a2c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -ab2 -a|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bd abd 0 a2c a2c ac2 ab2 b3  b2d b2d abd abc abc abc bc2 bc2 ac2 b2c b2c bcd |
|   0   0 -ad -ad 0   -ac -bc 0   0   0   -bd -bd -bd 0   0   0   -c2 -c2 0   |
|c  ac  0 -ab -ab ad  -a2 -ab bc  bc  ac  -b2 -b2 -b2 bd  bd  ad  -ac -ac c2  |
|a2 -a2 0 0   0   -ab 0   0   -ab -ab -a2 0   0   0   -b2 -b2 -ab 0   0   -ac |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| b2 bc bd c2 cd d2 bc-ad b3-a2c ac2-b2d c3-bd2 a3 a2b a2c a2d ab2 abc abd ac2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|bd 0 0 0 -bcd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -c2d -bcd -acd 0 0 0 0 0 0 0 |
|c  0 0 0 bc2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c3   bc2  ac2  0 0 0 0 0 0 0 |
|2  0 0 0 b2c  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 bc2  b2c  abc  0 0 0 0 0 0 0 |
|2b 0 0 0 -abc 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -ac2 -abc -a2c 0 0 0 0 0 0 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bcd bcd 0     bd2 c3  0 bd2 0 acd acd acd c2d c2d 0 0 0        0        0 0 0|
|0   0   cd    0   0   0 0   0 -d2 -d2 -d2 0   0   0 0 -acd     -acd     0 0 0|
|c2  c2  bc+ad cd  cd  0 cd  0 -bd -bd -bd d2  d2  0 0 -abc-a2d -abc-a2d 0 0 0|
|-ac -ac -ab   -ad -bc 0 -ad 0 0   0   0   -bd -bd 0 0 a2b      a2b      0 0 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| acd ad2 b3 b2c b2d bc2 bcd bd2 c3 c2d cd2 d3 |, | bc-ad b3-a2c ac2-b2d c3-bd|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d  a3 0  0  0  a2b 0   0   0   a2c 0   0   0   |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -c 0  a3 0  0  0   a2b 0   0   0   a2c 0   0   |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -b 0  0  a3 0  0   0   a2b 0   0   0   a2c 0   |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a  0  0  0  a3 0   0   0   a2b 0   0   0   a2c |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0 0 0 0 0 0 0 0 0 0 0        0 0        0        0 0 0 0 0 0 0       0 0 0 0|
| 0 0 0 0 0 0 0 0 0 0 -ac2+b2d 0 -bcd     -bcd     0 0 0 0 0 0 -c3+bd2 0 0 0 0|
| 0 0 0 0 0 0 0 0 0 0 b3-a2c   0 -b2c-abd -b2c-abd 0 0 0 0 0 0 0       0 0 0 0|
| 0 0 0 0 0 0 0 0 0 0 0        0 ab2      ab2      0 0 0 0 0 0 b3-a2c  0 0 0 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2 a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3 b2c b2d bc2 bcd bd2 c3 c2d cd2 d3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0|
|0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0|
|0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0|
|0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   a|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0 0 0 0 -b2 -ac -bd -c2 a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   |
| 0 0 0 0 c   d   0   0   0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d |
| 0 0 0 0 a   b   -c  -d  0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   |
| 0 0 0 0 0   0   a   b   0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| |)                                                                          |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|   acd 0   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0 |
|   0   acd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0 |
|   0   0   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0 |
|c2 0   0   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0|
|0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   a|
|a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0|
|0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  bc2 0   0   0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0  |
|  0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0  |
|  0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0  |
|d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0 |
|cd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc|
|   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0 |
|   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| cd2 0   0   0   d3 0  0  0  |, {4} | d  a3 0  0  0  a2b 0   0   0   a2c 0   |
| 0   cd2 0   0   0  d3 0  0  |  {4} | -c 0  a3 0  0  0   a2b 0   0   0   a2c |
| 0   0   cd2 0   0  0  d3 0  |  {4} | -b 0  0  a3 0  0   0   a2b 0   0   0   |
| 0   0   0   cd2 0  0  0  d3 |  {4} | a  0  0  0  a3 0   0   0   a2b 0   0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  0   0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0  |
|2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2|
|  bc2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0  |
|  0   bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0|
|0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   a|
|a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0|
|0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0   0   d3 0  0  0  |, {2} | -b2 -ac -bd -c2 a3 0  0  0  a2b 0   0   0   a2c|
| 0   0   0  d3 0  0  |  {3} | c   d   0   0   0  a3 0  0  0   a2b 0   0   0  |
| cd2 0   0  0  d3 0  |  {3} | a   b   -c  -d  0  0  a3 0  0   0   a2b 0   0  |
| 0   cd2 0  0  0  d3 |  {3} | 0   0   a   b   0  0  0  a3 0   0   0   a2b 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|   0   0   acd 0   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0 |
|c2 0   0   0   acd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2|
|   ac2 0   0   0   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0 |
|   0   ac2 0   0   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   |
| a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   |
| 0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   |
| 0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0  |
|d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d|
|  b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0  |
|  0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|ac2 0   0   0   acd 0   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b|
|0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0|
|0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0|
|0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   0   cd2 0   0   0   d3 0  0  0  |)                                      |
| 0   0   0   cd2 0   0   0  d3 0  0  |                                       |
| c2d 0   0   0   cd2 0   0  0  d3 0  |                                       |
| 0   c2d 0   0   0   cd2 0  0  0  d3 |                                       |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2|
|   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0 |
|   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0 |
|   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|--------------------------------------------+--------------------------------|
|                                            |subquotient ({5} | 0 0 0 0 0 0 a|
|                                            |                                |
|                                            |{-1, 4}                         |
|                                            |                                |
|                                            |                                |
|                                            |                                |
|--------------------------------------------+--------------------------------|
|d 0   0   0   cd2 0   0   0   d3 0  0  0  |)|subquotient ({4} | d  ad  0 0 -b|
|  c2d 0   0   0   cd2 0   0   0  d3 0  0  | |             {4} | -c -ac 0 0 bc|
|  0   c2d 0   0   0   cd2 0   0  0  d3 0  | |             {4} | -b -ab 0 0 b2|
|  0   0   c2d 0   0   0   cd2 0  0  0  d3 | |             {4} | a  a2  0 0 -a|
|                                            |                                |
|                                            |{-1, 3}                         |
|--------------------------------------------+--------------------------------|
|                                            |subquotient ({2} | ad ac ab a2 0|
|                                            |             {3} | 0  0  0  0  a|
|                                            |             {3} | 0  0  0  0  0|
|                                            |             {3} | 0  0  0  0  0|
|                                            |                                |
|                                            |{-1, 2}                         |
|--------------------------------------------+--------------------------------|
|                                            |subquotient (| a b c d bc-ad b3-|
|                                            |                                |
|                                            |{-1, 1}                         |
|                                            |                                |
|                                            |                                |
|                                            |                                |
|--------------------------------------------+--------------------------------|
|                                            |0                               |
|                                            |                                |
|                                            |{-1, 0}                         |
|--------------------------------------------+--------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d2 acd abd a2d ac2 abc a2c ab2 a2b a3 bd2 bcd b2d bc2 b2c b3 cd2 c2d c3 d3 a2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d 0 0 0 0 -cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ad2 acd abd a2d ac2 abc a2c ab2 a|
|  0 0 0 0 c2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0   0   0   0   0   0   0   0   0|
|  0 0 0 0 bc  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0   0   0   0   0   0   0   0   0|
|b 0 0 0 0 -ac 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0   0   0   0   0   0   0   0   0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0 0 bd bc b2 ab 0 0 0 cd c2 bc ac 0 0 0 d2 cd bd ad 0 0 0 -b2 -ac -bd -c2 a2|
| 0 0 0  0  0  0  b 0 0 0  0  0  0  c 0 0 0  0  0  0  d 0 0 c   d   0   0   0 |
| a 0 0  0  0  0  0 b 0 0  0  0  0  0 c 0 0  0  0  0  0 d 0 a   b   -c  -d  0 |
| 0 a 0  0  0  0  0 0 b 0  0  0  0  0 0 c 0  0  0  0  0 0 d 0   0   a   b   0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a2c ac2-b2d c3-bd2 a2 ab ac ad b2 bc bd c2 cd d2 |, | bc-ad b3-a2c ac2-b2d c3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| ab ac ad b2 bc bd c2 cd d2 |, {5} | a2 ab ac ad b2 bc bd c2 cd d2 |)        |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2b a3 0   0   0   0   0   0   0   0   0   0  0   0   0   0   0   0   0   0   |
|   0  ad2 acd abd a2d ac2 abc a2c ab2 a2b a3 0   0   0   0   0   0   0   0   |
|   0  0   0   0   0   0   0   0   0   0   0  ad2 acd abd a2d ac2 abc a2c ab2 |
|   0  0   0   0   0   0   0   0   0   0   0  0   0   0   0   0   0   0   0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0|
| a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0|
| 0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  b|
| 0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-bd2 a2 ab ac ad b2 bc bd c2 cd d2 |)                                        |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|0   0  0   0   0   0   0   0   bd2 bcd b2d bc2 b2c b3 0   0   0   0   0   0  |
|0   0  0   0   0   0   0   0   0   0   0   0   0   0  bd2 bcd b2d bc2 b2c b3 |
|a2b a3 0   0   0   0   0   0   0   0   0   0   0   0  0   0   0   0   0   0  |
|0   0  ad2 acd abd ac2 abc ab2 0   0   0   0   0   0  0   0   0   0   0   0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |, {2} | -b2 -ac -bd -c2 a2 0  0  0 |
|  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |  {3} | c   d   0   0   0  a2 0  0 |
|d 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |  {3} | a   b   -c  -d  0  0  a2 0 |
|  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |  {3} | 0   0   a   b   0  0  0  a2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|0   0   0   0   0   0   0   0   0  cd2 c2d c3 0   0   0   0  0   0   0  0  0 |
|0   0   0   0   0   0   0   0   0  0   0   0  cd2 0   0   0  0   0   0  d3 0 |
|bd2 bcd bc2 0   0   0   0   0   0  0   0   0  0   cd2 c2d c3 0   0   0  0  d3|
|0   0   0   bd2 bcd b2d bc2 b2c b3 0   0   0  0   0   0   0  cd2 c2d c3 0  0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0|
| 0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c|
| 0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0|
| 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0  d  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0|
| 0  -c 0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0|
| 0  -b 0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0|
| d3 a  0  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  b|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  0  0  cd 0  0  0  d2 0  0  0  |)                                           |
|2 0  0  0  cd 0  0  0  d2 0  0  |                                            |
|  c2 0  0  0  cd 0  0  0  d2 0  |                                            |
|  0  c2 0  0  0  cd 0  0  0  d2 |                                            |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |, {4} | d  a2 0  0  0  ab |
|  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |  {4} | -c 0  a2 0  0  0  |
|  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |  {4} | -b 0  0  a2 0  0  |
|c 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |  {4} | a  0  0  0  a2 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0 |
|ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0 |
|0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2|
|0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|------------------------------+----------------------------------------------|
|                              |0                                             |
|                              |                                              |
|                              |{0, 4}                                        |
|                              |                                              |
|                              |                                              |
|                              |                                              |
|------------------------------+----------------------------------------------|
| 0  cd 0  0  0  d2 0  0  0  |)|subquotient ({5} | d2 cd bd ad c2 bc ac b2 ab |
| 0  0  cd 0  0  0  d2 0  0  | |                                              |
| 0  0  0  cd 0  0  0  d2 0  | |{0, 3}                                        |
| c2 0  0  0  cd 0  0  0  d2 | |                                              |
|                              |                                              |
|                              |                                              |
|------------------------------+----------------------------------------------|
|                              |subquotient ({4} | d  d2 cd bd ad c2 bc ac b2 |
|                              |             {4} | -c 0  0  0  0  0  0  0  0  |
|                              |             {4} | -b 0  0  0  0  0  0  0  0  |
|                              |             {4} | a  0  0  0  0  0  0  0  0  |
|                              |                                              |
|                              |{0, 2}                                        |
|------------------------------+----------------------------------------------|
|                              |subquotient ({2} | d c b a 0 0 0 -b2 -ac -bd -|
|                              |             {3} | 0 0 0 0 1 0 0 c   d   0   0|
|                              |             {3} | 0 0 0 0 0 1 0 a   b   -c  -|
|                              |             {3} | 0 0 0 0 0 0 1 0   0   a   b|
|                              |                                              |
|                              |{0, 1}                                        |
|------------------------------+----------------------------------------------|
|                              |cokernel | bc-ad b3-a2c ac2-b2d c3-bd2 a b c d|
|                              |                                              |
|                              |{0, 0}                                        |
|------------------------------+----------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a2 a b c d |, {5} | a b c d |)                                               |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|ab a2 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  d2 cd bd ad c2 bc ac b2 ab a2 0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  d2 cd bd ad c2 bc ac b2 ab a2 0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  d2 cd bd c2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 |, {2} | -b2 -ac -bd -c2 a 0 0 0 b 0 0 0 c|
|   0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 |  {3} | c   d   0   0   0 a 0 0 0 b 0 0 0|
|d  0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 |  {3} | a   b   -c  -d  0 0 a 0 0 0 b 0 0|
|   0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d |  {3} | 0   0   a   b   0 0 0 a 0 0 0 b 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| |                                                                           |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0  0  d  a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 |, {4} | d  a 0 0 0 b 0 0 0 c 0 0 0|
| 0  0  -c 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 |  {4} | -c 0 a 0 0 0 b 0 0 0 c 0 0|
| 0  0  -b 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 |  {4} | -b 0 0 a 0 0 0 b 0 0 0 c 0|
| bc b2 a  0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d |  {4} | a  0 0 0 a 0 0 0 b 0 0 0 c|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0 0 0 d 0 0 0 |)                                                            |
| c 0 0 0 d 0 0 |                                                             |
| 0 c 0 0 0 d 0 |                                                             |
| 0 0 c 0 0 0 d |                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------+                                                                 |
|           |                                                                 |
|           |                                                                 |
|           |                                                                 |
|           |                                                                 |
|           |                                                                 |
|           |                                                                 |
|-----------+                                                                 |
|           |                                                                 |
|           |                                                                 |
|           |                                                                 |
|           |                                                                 |
|           |                                                                 |
|           |                                                                 |
|-----------+                                                                 |
| d 0 0 0 |)|                                                                 |
| 0 d 0 0 | |                                                                 |
| 0 0 d 0 | |                                                                 |
| 0 0 0 d | |                                                                 |
|           |                                                                 |
|           |                                                                 |
|-----------+                                                                 |
|           |                                                                 |
|           |                                                                 |
|           |                                                                 |
|           |                                                                 |
|           |                                                                 |
|           |                                                                 |
|-----------+                                                                 |
|           |                                                                 |
|           |                                                                 |
|           |                                                                 |
|-----------+                                                                 |
+-----------------------------------------------------------------------------+
|i8 : E^3                                                                     |
|                                                                             |
|     +-----------------------------------------------------------------------|
|o8 = |cokernel {4} | -d -b -d -c 0  0  -c 0  0  0  -d 0  0  0  0  -d -c 0  0 |
|     |         {4} | c  a  0  0  0  -d 0  -b 0  -d 0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  b  a  c  0  0  0  -d 0  0  -d 0  -d 0  0  0  0  0 |
|     |         {4} | 0  0  0  0  -d c  b  a  0  0  0  0  -d 0  -d 0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  c  b  a  0  0  0  0  0  0  0  -d|
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  b  a  0  0  0  0  c  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  d  c  b  a  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -d c |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |                                                                       |
|     |{-4, 4}                                                                |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 3}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 2}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 1}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 0}                                                                |
|     +-----------------------------------------------------------------------|
|                                                                             |
|o8 : SpectralSequencePage                                                    |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  -d 0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  -d 0  0  0  -d 0  0  0  0  -d 0  0  0  0  -d 0  0  0  0  0  0  0|
| -d 0  0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  -d 0  0  0  0  -d 0  0  0|
| 0  0  -d 0  0  -d 0  0  0  0  0  -d 0  0  0  0  -d 0  0  0  0  0  0  0  0  -|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| b  a  0  0  0  0  -d 0  0  0  0  0  -d 0  0  0  0  0  0  0  0  -d 0  0  0  0|
| 0  0  c  b  a  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  -d 0  0  0  0  0|
| 0  0  0  0  0  b  a  0  0  0  0  0  0  0  0  0  0  0  0  c  0  0  0  -d 0  0|
| 0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -d c  b  a  0  -d 0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  d  c  b|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|d 0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  -d 0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  -d 0  0  0  -d 0  0  0  0  0  0  -d 0  0  0  -d 0  0  -d 0  0  0  0  -d |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  -d 0  0  0  0  |
|  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  c  b  a  -d 0  0  0  -d 0  0  0  0  0  0  -d 0  0  0  0  0  0  0  -d 0  |
|  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  c  b  a  -d 0  0  0  0  0  0  -d 0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  c  b  a  -d 0  0  -d 0  0  0  0  -d 0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  0  0  0  0  -d 0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  d  c  b  a  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|----------------------------+------------------------------------------------|
|0  0  0  0  0  0  0  0  0  ||0                                               |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||{-3, 4}                                         |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  -d 0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  -d 0  0  0  -d 0  0  0  ||                                                |
|0  0  0  0  -d 0  0  0  -d ||                                                |
|-d 0  0  0  0  0  0  -d 0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|c  b  a  -d 0  0  0  0  0  ||                                                |
|0  0  0  c  b  a  -d 0  0  ||                                                |
|0  0  0  0  0  0  c  b  a  ||                                                |
|                            |                                                |
|                            |                                                |
|----------------------------+------------------------------------------------|
|                            |cokernel {3} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                            |         {3} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0|
|                            |         {3} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0|
|                            |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0|
|                            |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d|
|                            |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                            |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                            |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                            |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                            |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                            |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                            |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                            |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                            |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                            |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                            |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                            |                                                |
|                            |{-3, 3}                                         |
|----------------------------+------------------------------------------------|
|                            |0                                               |
|                            |                                                |
|                            |{-3, 2}                                         |
|                            |                                                |
|                            |                                                |
|                            |                                                |
|                            |                                                |
|                            |                                                |
|                            |                                                |
|                            |                                                |
|                            |                                                |
|----------------------------+------------------------------------------------|
|                            |0                                               |
|                            |                                                |
|                            |{-3, 1}                                         |
|                            |                                                |
|                            |                                                |
|                            |                                                |
|----------------------------+------------------------------------------------|
|                            |0                                               |
|                            |                                                |
|                            |{-3, 0}                                         |
|----------------------------+------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-------------------+---------------------------------------------------------|
|                   |0                                                        |
|                   |                                                         |
|                   |{-2, 4}                                                  |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|-------------------+---------------------------------------------------------|
|0 0 0 0 0 0 0 0 0 ||0                                                        |
|0 0 0 0 0 0 0 0 0 ||                                                         |
|0 0 0 0 0 0 0 0 0 ||{-2, 3}                                                  |
|0 0 0 0 0 0 0 0 0 ||                                                         |
|0 0 0 0 0 0 0 0 0 ||                                                         |
|0 0 0 0 0 0 0 0 0 ||                                                         |
|0 0 0 0 0 0 0 0 0 ||                                                         |
|0 0 0 0 0 0 0 0 0 ||                                                         |
|0 0 0 0 0 0 0 0 0 ||                                                         |
|0 0 0 0 0 0 0 0 0 ||                                                         |
|0 0 0 0 0 0 0 0 0 ||                                                         |
|0 0 0 0 0 0 0 0 0 ||                                                         |
|0 0 0 0 0 0 0 0 0 ||                                                         |
|a 0 0 0 0 0 0 0 0 ||                                                         |
|0 d c b a 0 0 0 0 ||                                                         |
|0 0 0 0 0 d c b a ||                                                         |
|                   |                                                         |
|                   |                                                         |
|-------------------+---------------------------------------------------------|
|                   |cokernel {2} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|                   |         {2} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|                   |         {2} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 |
|                   |         {2} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 |
|                   |         {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 |
|                   |         {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d |
|                   |         {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|                   |         {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|                   |         {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|                   |                                                         |
|                   |{-2, 2}                                                  |
|-------------------+---------------------------------------------------------|
|                   |0                                                        |
|                   |                                                         |
|                   |{-2, 1}                                                  |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|-------------------+---------------------------------------------------------|
|                   |0                                                        |
|                   |                                                         |
|                   |{-2, 0}                                                  |
|-------------------+---------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-------------------------------+---------------------------------------------|
|                               |0                                            |
|                               |                                             |
|                               |{-1, 4}                                      |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|-------------------------------+---------------------------------------------|
|                               |0                                            |
|                               |                                             |
|                               |{-1, 3}                                      |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|-------------------------------+---------------------------------------------|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||cokernel {4} | d c b a 0 0 0 0 0 0 0 0 0 0 0 |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||         {4} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||         {4} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||         {4} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||         {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|c b a 0 0 0 0 0 0 0 0 0 0 0 0 ||         {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|0 0 0 d c b a 0 0 0 0 0 0 0 0 ||         {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|0 0 0 0 0 0 0 d c b a 0 0 0 0 ||         {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|0 0 0 0 0 0 0 0 0 0 0 d c b a ||                                             |
|                               |{-1, 2}                                      |
|                               |                                             |
|-------------------------------+---------------------------------------------|
|                               |cokernel {1} | d c b a 0 0 0 0 0 0 0 0 0 0 0 |
|                               |         {1} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 |
|                               |         {1} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 |
|                               |         {1} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b |
|                               |                                             |
|                               |{-1, 1}                                      |
|-------------------------------+---------------------------------------------|
|                               |0                                            |
|                               |                                             |
|                               |{-1, 0}                                      |
|-------------------------------+---------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------+----------------------------------------+|
|                                   |0                                       ||
|                                   |                                        ||
|                                   |{0, 4}                                  ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|-----------------------------------+----------------------------------------+|
|                                   |0                                       ||
|                                   |                                        ||
|                                   |{0, 3}                                  ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|-----------------------------------+----------------------------------------+|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||0                                       ||
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                                        ||
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||{0, 2}                                  ||
|a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                                        ||
|0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 ||                                        ||
|0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 ||                                        ||
|0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 ||                                        ||
|0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a ||                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|-----------------------------------+----------------------------------------+|
|0 |                                |cokernel {3} | d c b a 0 0 0 0 0 0 0 0 |||
|0 |                                |         {3} | 0 0 0 0 d c b a 0 0 0 0 |||
|0 |                                |         {3} | 0 0 0 0 0 0 0 0 d c b a |||
|a |                                |                                        ||
|                                   |{0, 1}                                  ||
|                                   |                                        ||
|-----------------------------------+----------------------------------------+|
|                                   |cokernel | d c b a |                    ||
|                                   |                                        ||
|                                   |{0, 0}                                  ||
|-----------------------------------+----------------------------------------+|
+-----------------------------------------------------------------------------+

See also
========

  * minimalPresentation(SpectralSequencePage)
    -- a minimal presentation of
    a spectral sequence page
  * prune(SpectralSequencePage)
    -- a minimal presentation of
    a spectral sequence page
  * minimalPresentation (Macaulay2Doc) -- compute a
    minimal presentation
  * prune (Macaulay2Doc) -- prune, e.g., compute a minimal
    presentation
  * pruningMaps -- compute the pruning maps on a spectral
    sequence page

Ways to use this method:
========================

  * minimalPresentation(SpectralSequence)
    -- a minimal presentation of a
    spectral sequence
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:3125:0.

minimalPresentation(SpectralSequencePage) -- a minimal presentation of a spectral sequence page
***********************************************************************************************

  * Function: minimalPresentation (Macaulay2Doc),
  * Usage:
        E = minimalPresentation e
  * Inputs:
      * e, a spectral sequence page,
  * Optional inputs (Macaulay2Doc),:
      * Exclude (Macaulay2Doc), => ...,
        default value {},
  * Outputs:
      * E, a spectral sequence page,

Description
===========

Returns a minimal presentation of the spectral sequence page.

If we fail to prune a spectral sequence then the out-put can be highly
unintelligible.

As a specific example consider the filtered complex $K$ below, obtained by
multiplying the minimal free resolution of the rational quartic space curve by
successive powers of the irrelevant ideal.

+----------------------------------------------------+
|i1 : B = QQ[a..d];                                  |
+----------------------------------------------------+
|i2 : J = ideal vars B;                              |
|                                                    |
|o2 : Ideal of B                                     |
+----------------------------------------------------+
|i3 : C = complete res monomialCurveIdeal(B,{1,3,4});|
+----------------------------------------------------+
|i4 : K = filteredComplex(J,C,4);                    |
+----------------------------------------------------+

Compare some pruned and non-prunded pages the spectral sequence $E$ below.

+-----------------------------------------------------------------------------+
|i5 : E = spectralSequence K;                                                 |
+-----------------------------------------------------------------------------+
|i6 : E^3                                                                     |
|                                                                             |
|     +-----------------------------------------------------------------------|
|o6 = |subquotient (| a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab|
|     |                                                                       |
|     |{-4, 4}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 3}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 2}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 1}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 0}                                                                |
|     +-----------------------------------------------------------------------|
|                                                                             |
|o6 : SpectralSequencePage                                                    |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d3 c4 c3d c2d2 cd3 d4 a2bc-a3d a2b3-a4c a3c2-a2b2d a2c3-a2bd2 ab2c-a2bd ab4-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|3bc a2bc2-ab3d abc3-ab2d2 abc2-a2cd ab3c-a3c2 a2c3-ab2cd ac4-abcd2 abcd-a2d2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|ab3d-a3cd a2c2d-ab2d2 ac3d-abd3 b3c-ab2d b5-a2b2c ab2c2-b4d b2c3-b3d2 b2c2-ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|cd b4c-a2bc2 abc3-b3cd bc4-b2cd2 b2cd-abd2 b4d-a2bcd abc2d-b3d2 bc3d-b2d3 bc3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-ac2d b3c2-a2c3 ac4-b2c2d c5-bc2d2 bc2d-acd2 b3cd-a2c2d ac3d-b2cd2 c4d-bcd3 b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|cd2-ad3 b3d2-a2cd2 ac2d2-b2d3 c3d2-bd4 0 |, | a2bc-a3d a2b3-a4c a3c2-a2b2d a2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c3-a2bd2 ab2c-a2bd ab4-a3bc a2bc2-ab3d abc3-ab2d2 abc2-a2cd ab3c-a3c2 a2c3-ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2cd ac4-abcd2 abcd-a2d2 ab3d-a3cd a2c2d-ab2d2 ac3d-abd3 b3c-ab2d b5-a2b2c ab2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c2-b4d b2c3-b3d2 b2c2-abcd b4c-a2bc2 abc3-b3cd bc4-b2cd2 b2cd-abd2 b4d-a2bcd |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|abc2d-b3d2 bc3d-b2d3 bc3-ac2d b3c2-a2c3 ac4-b2c2d c5-bc2d2 bc2d-acd2 b3cd-a2c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-------------------------------------------------------------------+---------|
|2d ac3d-b2cd2 c4d-bcd3 bcd2-ad3 b3d2-a2cd2 ac2d2-b2d3 c3d2-bd4 0 |)|subquotie|
|                                                                   |         |
|                                                                   |         |
|                                                                   |         |
|                                                                   |         |
|                                                                   |{-3, 4}  |
|-------------------------------------------------------------------+---------|
|                                                                   |subquotie|
|                                                                   |         |
|                                                                   |{-3, 3}  |
|                                                                   |         |
|                                                                   |         |
|                                                                   |         |
|-------------------------------------------------------------------+---------|
|                                                                   |0        |
|                                                                   |         |
|                                                                   |{-3, 2}  |
|                                                                   |         |
|                                                                   |         |
|                                                                   |         |
|-------------------------------------------------------------------+---------|
|                                                                   |0        |
|                                                                   |         |
|                                                                   |{-3, 1}  |
|                                                                   |         |
|                                                                   |         |
|                                                                   |         |
|-------------------------------------------------------------------+---------|
|                                                                   |0        |
|                                                                   |         |
|                                                                   |{-3, 0}  |
|-------------------------------------------------------------------+---------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|nt ({2} | 0 a2b2 a2bd a2bd 0 a3c  a3c  a2c2 a2b2 ab3  ab2d ab2d a2bd a2bc a2b|
|    {3} | 0 -a2c 0    0    0 -a2d -a2d 0    -a2c -abc 0    0    0    -abd -ab|
|    {3} | 0 -a3  a2c  a2c  0 -a2b -a2b a2d  -a3  -a2b abc  abc  a2c  -ab2 -ab|
|    {3} | 0 0    -a3  -a3  0 0    0    -a2b 0    0    -a2b -a2b -a3  0    0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|nt (| a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3 b2c b2d bc2 bcd bd2 c3 c2d cd|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c a2bc abc2 abc2 a2c2 ab2c ab2c abcd abcd abcd 0       abd2 ac3  abd2 0 a2cd |
|d -abd 0    0    0    -ac2 -ac2 0    0    0    acd     0    0    0    0 -ad2 |
|2 -ab2 abd  abd  a2d  -a2c -a2c ac2  ac2  ac2  abc+a2d acd  acd  acd  0 -abd |
|  0    -ab2 -ab2 -a2b 0    0    -a2c -a2c -a2c -a2b    -a2d -abc -a2d 0 0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2 d3 abc-a2d ab3-a3c a2c2-ab2d ac3-abd2 b2c-abd b4-a2bc abc2-b3d bc3-b2d2 bc2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|a2cd a2cd ac2d ac2d ab3  ab2c b4   b3d  b3d  ab2d 0        b2c2 b2c2 abc2 b3c|
|-ad2 -ad2 0    0    -abc -ac2 -b2c 0    0    0    -ac2+b2d 0    0    0    -bc|
|-abd -abd ad2  ad2  -a2b -a2c -ab2 b2c  b2c  abc  b3-a2c   b2d  b2d  abd  -ab|
|0    0    -abd -abd 0    0    0    -ab2 -ab2 -a2b 0        -b3  -b3  -ab2 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-acd b3c-a2c2 ac3-b2cd c4-bcd2 bcd-ad2 b3d-a2cd ac2d-b2d2 c3d-bd3 a4 a3b a3c |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  b3c  b2cd b2cd b2cd abcd 0       b2d2 bc3  b2d2 abd2 0       bc2d bc2d bc3 |
|2 -bc2 0    0    0    0    bcd     0    0    0    0    bd2     0    0    0   |
|c -abc bc2  bc2  bc2  ac2  b2c+abd bcd  bcd  bcd  acd  ac2+b2d bd2  bd2  bcd |
|  0    -abc -abc -abc -a2c -ab2    -abd -b2c -abd -a2d -a2c    -b2d -b2d -b2c|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab2d abc2 abcd abd2 ac3 ac2d acd2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| ac3  0       0        bc2d ac2d 0       bcd2 bcd2 c4   bcd2 0       bd3  c3d|
| 0    c3      0        0    0    c2d     0    0    0    0    cd2     0    0  |
| acd  ac2+b2d c3-bd2   bd2  ad2  bc2+acd c2d  c2d  c2d  c2d  bcd+ad2 cd2  cd2|
| -abc -b3     -ac2+b2d -b2d -abd -abc    -acd -acd -bc2 -acd -abd    -ad2 -bc|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 bd3 c4 c3d c2d2 cd3 d4 |, | abc-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  c3d  0 bd3  0 acd2 acd2 acd2 c2d2 c2d2 0 0 0         0         0 0 0 0 0 0 |
|  0    0 0    0 -d3  -d3  -d3  0    0    0 0 -a2cd     -a2cd     0 0 0 0 0 0 |
|  cd2  0 cd2  0 -bd2 -bd2 -bd2 d3   d3   0 0 -a2bc-a3d -a2bc-a3d 0 0 0 0 0 0 |
|d -bcd 0 -ad2 0 0    0    0    -bd2 -bd2 0 0 a3b       a3b       0 0 0 0 0 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2d ab3-a3c a2c2-ab2d ac3-abd2 b2c-abd b4-a2bc abc2-b3d bc3-b2d2 bc2-acd b3c-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0 0 0 0 0 0 0 0          0 0          0          0 0 0 0 0 0 0         0 0 0 |
|0 0 0 0 0 0 0 -a2c2+ab2d 0 -abcd      -abcd      0 0 0 0 0 0 -ac3+abd2 0 0 0 |
|0 0 0 0 0 0 0 ab3-a3c    0 -ab2c-a2bd -ab2c-a2bd 0 0 0 0 0 0 0         0 0 0 |
|0 0 0 0 0 0 0 0          0 a2b2       a2b2       0 0 0 0 0 0 ab3-a3c   0 0 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2c2 ac3-b2cd c4-bcd2 bcd-ad2 b3d-a2cd ac2d-b2d2 c3d-bd3 a4 a3b a3c a3d a2b2 a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0 0 0 0 0 0 0         0          0         0              0 0 0 0 0 0        |
|0 0 0 0 0 0 -abc2+b3d -a2c2+ab2d -ac3+abd2 -ac3+b2cd+abd2 0 0 0 0 0 -bc3+ac2d|
|0 0 0 0 0 0 b4-a2bc   ab3-a3c    0         b3c+ab2d       0 0 0 0 0 -b3d+a2cd|
|0 0 0 0 0 0 0         0          ab3-a3c   -a3c           0 0 0 0 0 b4-a2bc  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -ab2 -a2c -abd -ac2 -b3 -abc -b2d -bc2 -b2c -ac2|
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ac   ad   0    0    bc  bd   0    0    c2   cd  |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a2   ab   -ac  -ad  ab  b2   -bc  -bd  ac   bc  |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0    0    a2   ab   0   0    ab   b2   0    0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 bd3 c4 c3d c2d2 cd3 d4 |)                  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| -bcd -c3 -b2d -acd -bd2 -c2d a4 0  0  0  a3b 0   0   0   a3c 0   0   0   a3d|
| 0    0   cd   d2   0    0    0  a4 0  0  0   a3b 0   0   0   a3c 0   0   0  |
| -c2  -cd ad   bd   -cd  -d2  0  0  a4 0  0   0   a3b 0   0   0   a3c 0   0  |
| ac   bc  0    0    ad   bd   0  0  0  a4 0   0   0   a3b 0   0   0   a3c 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   0   0   a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    a2c2|
| a3d 0   0   0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0   |
| 0   a3d 0   0    0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0   |
| 0   0   a3d 0    0    0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0    0    0    a2cd 0    0    0    a2d2 0    0    0    ab3 0   0   0   ab2c |
| a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0    0   ab3 0   0   0    |
| 0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0   0   ab3 0   0    |
| 0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0   0   0   ab3 0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0    ab|
|ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0 |
|0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0 |
|0    0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d2 0    0    0    ac3 0   0   0   ac2d 0    0    0    acd2 0    0    0    ad3|
|   abd2 0    0    0   ac3 0   0   0    ac2d 0    0    0    acd2 0    0    0  |
|   0    abd2 0    0   0   ac3 0   0    0    ac2d 0    0    0    acd2 0    0  |
|   0    0    abd2 0   0   0   ac3 0    0    0    ac2d 0    0    0    acd2 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   0   0   b4 0  0  0  b3c 0   0   0   b3d 0   0   0   b2c2 0    0    0    |
| ad3 0   0   0  b4 0  0  0   b3c 0   0   0   b3d 0   0   0    b2c2 0    0    |
| 0   ad3 0   0  0  b4 0  0   0   b3c 0   0   0   b3d 0   0    0    b2c2 0    |
| 0   0   ad3 0  0  0  b4 0   0   0   b3c 0   0   0   b3d 0    0    0    b2c2 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|b2cd 0    0    0    b2d2 0    0    0    bc3 0   0   0   bc2d 0    0    0    b|
|0    b2cd 0    0    0    b2d2 0    0    0   bc3 0   0   0    bc2d 0    0    0|
|0    0    b2cd 0    0    0    b2d2 0    0   0   bc3 0   0    0    bc2d 0    0|
|0    0    0    b2cd 0    0    0    b2d2 0   0   0   bc3 0    0    0    bc2d 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|cd2 0    0    0    bd3 0   0   0   c4 0  0  0  c3d 0   0   0   c2d2 0    0   |
|    bcd2 0    0    0   bd3 0   0   0  c4 0  0  0   c3d 0   0   0    c2d2 0   |
|    0    bcd2 0    0   0   bd3 0   0  0  c4 0  0   0   c3d 0   0    0    c2d2|
|    0    0    bcd2 0   0   0   bd3 0  0  0  c4 0   0   0   c3d 0    0    0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0    cd3 0   0   0   d4 0  0  0  |, {2} | -ab2 -a2c -abd -ac2 -b3 -abc -b2d |
| 0    0   cd3 0   0   0  d4 0  0  |  {3} | ac   ad   0    0    bc  bd   0    |
| 0    0   0   cd3 0   0  0  d4 0  |  {3} | a2   ab   -ac  -ad  ab  b2   -bc  |
| c2d2 0   0   0   cd3 0  0  0  d4 |  {3} | 0    0    a2   ab   0   0    ab   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-bc2 -b2c -ac2 -bcd -c3 -b2d -acd -bd2 -c2d a4 0  0  0  a3b 0   0   0   a3c 0|
|0    c2   cd   0    0   cd   d2   0    0    0  a4 0  0  0   a3b 0   0   0   a|
|-bd  ac   bc   -c2  -cd ad   bd   -cd  -d2  0  0  a4 0  0   0   a3b 0   0   0|
|b2   0    0    ac   bc  0    0    ad   bd   0  0  0  a4 0   0   0   a3b 0   0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|   0   0   a3d 0   0   0   a2b2 0    0    0    a2bc 0    0    0    a2bd 0    |
|3c 0   0   0   a3d 0   0   0    a2b2 0    0    0    a2bc 0    0    0    a2bd |
|   a3c 0   0   0   a3d 0   0    0    a2b2 0    0    0    a2bc 0    0    0    |
|   0   a3c 0   0   0   a3d 0    0    0    a2b2 0    0    0    a2bc 0    0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0    0    ab3 0  |
|0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0    0   ab3|
|a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0   0  |
|0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0   0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   0   ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0  |
| 0   0   0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abc|
| ab3 0   0    0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0  |
| 0   ab3 0    0    0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  0    0    abd2 0    0    0    ac3 0   0   0   ac2d 0    0    0    acd2 0   |
|d 0    0    0    abd2 0    0    0   ac3 0   0   0    ac2d 0    0    0    acd2|
|  abcd 0    0    0    abd2 0    0   0   ac3 0   0    0    ac2d 0    0    0   |
|  0    abcd 0    0    0    abd2 0   0   0   ac3 0    0    0    ac2d 0    0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0    0    ad3 0   0   0   b4 0  0  0  b3c 0   0   0   b3d 0   0   0   b2c2 0|
| 0    0    0   ad3 0   0   0  b4 0  0  0   b3c 0   0   0   b3d 0   0   0    b|
| acd2 0    0   0   ad3 0   0  0  b4 0  0   0   b3c 0   0   0   b3d 0   0    0|
| 0    acd2 0   0   0   ad3 0  0  0  b4 0   0   0   b3c 0   0   0   b3d 0    0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|    0    0    b2cd 0    0    0    b2d2 0    0    0    bc3 0   0   0   bc2d 0 |
|2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0   bc3 0   0   0    bc|
|    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0   0   bc3 0   0    0 |
|    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0   0   0   bc3 0    0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|   0    0    bcd2 0    0    0    bd3 0   0   0   c4 0  0  0  c3d 0   0   0   |
|2d 0    0    0    bcd2 0    0    0   bd3 0   0   0  c4 0  0  0   c3d 0   0   |
|   bc2d 0    0    0    bcd2 0    0   0   bd3 0   0  0  c4 0  0   0   c3d 0   |
|   0    bc2d 0    0    0    bcd2 0   0   0   bd3 0  0  0  c4 0   0   0   c3d |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|--------------------------------------------------+--------------------------|
|c2d2 0    0    0    cd3 0   0   0   d4 0  0  0  |)|subquotient ({4} | ad  bd |
|0    c2d2 0    0    0   cd3 0   0   0  d4 0  0  | |             {4} | -ac -bc|
|0    0    c2d2 0    0   0   cd3 0   0  0  d4 0  | |             {4} | -ab -b2|
|0    0    0    c2d2 0   0   0   cd3 0  0  0  d4 | |             {4} | a2  ab |
|                                                  |                          |
|                                                  |{-2, 4}                   |
|--------------------------------------------------+--------------------------|
|                                                  |subquotient ({2} | 0 ab2 a|
|                                                  |             {3} | 0 -ac 0|
|                                                  |             {3} | 0 -a2 a|
|                                                  |             {3} | 0 0   -|
|                                                  |                          |
|                                                  |{-2, 3}                   |
|--------------------------------------------------+--------------------------|
|                                                  |subquotient (| a2 ab ac ad|
|                                                  |                          |
|                                                  |{-2, 2}                   |
|                                                  |                          |
|                                                  |                          |
|                                                  |                          |
|--------------------------------------------------+--------------------------|
|                                                  |0                         |
|                                                  |                          |
|                                                  |{-2, 1}                   |
|                                                  |                          |
|                                                  |                          |
|                                                  |                          |
|--------------------------------------------------+--------------------------|
|                                                  |0                         |
|                                                  |                          |
|                                                  |{-2, 0}                   |
|--------------------------------------------------+--------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| cd  d2  a2d  0 0 -abd 0 0 0 0 -acd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -b2d -a|
| -c2 -cd -a2c 0 0 abc  0 0 0 0 ac2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b2c  ab|
| -bc -bd -a2b 0 0 ab2  0 0 0 0 abc  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b3   ab|
| ac  ad  a3   0 0 -a2b 0 0 0 0 -a2c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -ab2 -a|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bd abd 0 a2c a2c ac2 ab2 b3  b2d b2d abd abc abc abc bc2 bc2 ac2 b2c b2c bcd |
|   0   0 -ad -ad 0   -ac -bc 0   0   0   -bd -bd -bd 0   0   0   -c2 -c2 0   |
|c  ac  0 -ab -ab ad  -a2 -ab bc  bc  ac  -b2 -b2 -b2 bd  bd  ad  -ac -ac c2  |
|a2 -a2 0 0   0   -ab 0   0   -ab -ab -a2 0   0   0   -b2 -b2 -ab 0   0   -ac |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| b2 bc bd c2 cd d2 bc-ad b3-a2c ac2-b2d c3-bd2 a3 a2b a2c a2d ab2 abc abd ac2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|bd 0 0 0 -bcd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -c2d -bcd -acd 0 0 0 0 0 0 0 |
|c  0 0 0 bc2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c3   bc2  ac2  0 0 0 0 0 0 0 |
|2  0 0 0 b2c  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 bc2  b2c  abc  0 0 0 0 0 0 0 |
|2b 0 0 0 -abc 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -ac2 -abc -a2c 0 0 0 0 0 0 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bcd bcd 0     bd2 c3  0 bd2 0 acd acd acd c2d c2d 0 0 0        0        0 0 0|
|0   0   cd    0   0   0 0   0 -d2 -d2 -d2 0   0   0 0 -acd     -acd     0 0 0|
|c2  c2  bc+ad cd  cd  0 cd  0 -bd -bd -bd d2  d2  0 0 -abc-a2d -abc-a2d 0 0 0|
|-ac -ac -ab   -ad -bc 0 -ad 0 0   0   0   -bd -bd 0 0 a2b      a2b      0 0 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| acd ad2 b3 b2c b2d bc2 bcd bd2 c3 c2d cd2 d3 |, | bc-ad b3-a2c ac2-b2d c3-bd|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d  a3 0  0  0  a2b 0   0   0   a2c 0   0   0   |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -c 0  a3 0  0  0   a2b 0   0   0   a2c 0   0   |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -b 0  0  a3 0  0   0   a2b 0   0   0   a2c 0   |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a  0  0  0  a3 0   0   0   a2b 0   0   0   a2c |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0 0 0 0 0 0 0 0 0 0 0        0 0        0        0 0 0 0 0 0 0       0 0 0 0|
| 0 0 0 0 0 0 0 0 0 0 -ac2+b2d 0 -bcd     -bcd     0 0 0 0 0 0 -c3+bd2 0 0 0 0|
| 0 0 0 0 0 0 0 0 0 0 b3-a2c   0 -b2c-abd -b2c-abd 0 0 0 0 0 0 0       0 0 0 0|
| 0 0 0 0 0 0 0 0 0 0 0        0 ab2      ab2      0 0 0 0 0 0 b3-a2c  0 0 0 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2 a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3 b2c b2d bc2 bcd bd2 c3 c2d cd2 d3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0|
|0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0|
|0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0|
|0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   a|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0 0 0 0 -b2 -ac -bd -c2 a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   |
| 0 0 0 0 c   d   0   0   0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d |
| 0 0 0 0 a   b   -c  -d  0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   |
| 0 0 0 0 0   0   a   b   0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| |)                                                                          |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|   acd 0   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0 |
|   0   acd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0 |
|   0   0   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0 |
|c2 0   0   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0|
|0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   a|
|a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0|
|0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  bc2 0   0   0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0  |
|  0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0  |
|  0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0  |
|d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0 |
|cd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc|
|   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0 |
|   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| cd2 0   0   0   d3 0  0  0  |, {4} | d  a3 0  0  0  a2b 0   0   0   a2c 0   |
| 0   cd2 0   0   0  d3 0  0  |  {4} | -c 0  a3 0  0  0   a2b 0   0   0   a2c |
| 0   0   cd2 0   0  0  d3 0  |  {4} | -b 0  0  a3 0  0   0   a2b 0   0   0   |
| 0   0   0   cd2 0  0  0  d3 |  {4} | a  0  0  0  a3 0   0   0   a2b 0   0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  0   0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0  |
|2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2|
|  bc2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0  |
|  0   bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0|
|0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   a|
|a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0|
|0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0   0   d3 0  0  0  |, {2} | -b2 -ac -bd -c2 a3 0  0  0  a2b 0   0   0   a2c|
| 0   0   0  d3 0  0  |  {3} | c   d   0   0   0  a3 0  0  0   a2b 0   0   0  |
| cd2 0   0  0  d3 0  |  {3} | a   b   -c  -d  0  0  a3 0  0   0   a2b 0   0  |
| 0   cd2 0  0  0  d3 |  {3} | 0   0   a   b   0  0  0  a3 0   0   0   a2b 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|   0   0   acd 0   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0 |
|c2 0   0   0   acd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2|
|   ac2 0   0   0   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0 |
|   0   ac2 0   0   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   |
| a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   |
| 0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   |
| 0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0  |
|d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d|
|  b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0  |
|  0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|ac2 0   0   0   acd 0   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b|
|0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0|
|0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0|
|0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   0   cd2 0   0   0   d3 0  0  0  |)                                      |
| 0   0   0   cd2 0   0   0  d3 0  0  |                                       |
| c2d 0   0   0   cd2 0   0  0  d3 0  |                                       |
| 0   c2d 0   0   0   cd2 0  0  0  d3 |                                       |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2|
|   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0 |
|   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0 |
|   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|--------------------------------------------+--------------------------------|
|                                            |subquotient ({5} | 0 0 0 0 0 0 a|
|                                            |                                |
|                                            |{-1, 4}                         |
|                                            |                                |
|                                            |                                |
|                                            |                                |
|--------------------------------------------+--------------------------------|
|d 0   0   0   cd2 0   0   0   d3 0  0  0  |)|subquotient ({4} | d  ad  0 0 -b|
|  c2d 0   0   0   cd2 0   0   0  d3 0  0  | |             {4} | -c -ac 0 0 bc|
|  0   c2d 0   0   0   cd2 0   0  0  d3 0  | |             {4} | -b -ab 0 0 b2|
|  0   0   c2d 0   0   0   cd2 0  0  0  d3 | |             {4} | a  a2  0 0 -a|
|                                            |                                |
|                                            |{-1, 3}                         |
|--------------------------------------------+--------------------------------|
|                                            |subquotient ({2} | ad ac ab a2 0|
|                                            |             {3} | 0  0  0  0  a|
|                                            |             {3} | 0  0  0  0  0|
|                                            |             {3} | 0  0  0  0  0|
|                                            |                                |
|                                            |{-1, 2}                         |
|--------------------------------------------+--------------------------------|
|                                            |subquotient (| a b c d bc-ad b3-|
|                                            |                                |
|                                            |{-1, 1}                         |
|                                            |                                |
|                                            |                                |
|                                            |                                |
|--------------------------------------------+--------------------------------|
|                                            |0                               |
|                                            |                                |
|                                            |{-1, 0}                         |
|--------------------------------------------+--------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d2 acd abd a2d ac2 abc a2c ab2 a2b a3 bd2 bcd b2d bc2 b2c b3 cd2 c2d c3 d3 a2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d 0 0 0 0 -cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ad2 acd abd a2d ac2 abc a2c ab2 a|
|  0 0 0 0 c2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0   0   0   0   0   0   0   0   0|
|  0 0 0 0 bc  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0   0   0   0   0   0   0   0   0|
|b 0 0 0 0 -ac 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0   0   0   0   0   0   0   0   0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0 0 bd bc b2 ab 0 0 0 cd c2 bc ac 0 0 0 d2 cd bd ad 0 0 0 -b2 -ac -bd -c2 a2|
| 0 0 0  0  0  0  b 0 0 0  0  0  0  c 0 0 0  0  0  0  d 0 0 c   d   0   0   0 |
| a 0 0  0  0  0  0 b 0 0  0  0  0  0 c 0 0  0  0  0  0 d 0 a   b   -c  -d  0 |
| 0 a 0  0  0  0  0 0 b 0  0  0  0  0 0 c 0  0  0  0  0 0 d 0   0   a   b   0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a2c ac2-b2d c3-bd2 a2 ab ac ad b2 bc bd c2 cd d2 |, | bc-ad b3-a2c ac2-b2d c3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| ab ac ad b2 bc bd c2 cd d2 |, {5} | a2 ab ac ad b2 bc bd c2 cd d2 |)        |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2b a3 0   0   0   0   0   0   0   0   0   0  0   0   0   0   0   0   0   0   |
|   0  ad2 acd abd a2d ac2 abc a2c ab2 a2b a3 0   0   0   0   0   0   0   0   |
|   0  0   0   0   0   0   0   0   0   0   0  ad2 acd abd a2d ac2 abc a2c ab2 |
|   0  0   0   0   0   0   0   0   0   0   0  0   0   0   0   0   0   0   0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0|
| a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0|
| 0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  b|
| 0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-bd2 a2 ab ac ad b2 bc bd c2 cd d2 |)                                        |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|0   0  0   0   0   0   0   0   bd2 bcd b2d bc2 b2c b3 0   0   0   0   0   0  |
|0   0  0   0   0   0   0   0   0   0   0   0   0   0  bd2 bcd b2d bc2 b2c b3 |
|a2b a3 0   0   0   0   0   0   0   0   0   0   0   0  0   0   0   0   0   0  |
|0   0  ad2 acd abd ac2 abc ab2 0   0   0   0   0   0  0   0   0   0   0   0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |, {2} | -b2 -ac -bd -c2 a2 0  0  0 |
|  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |  {3} | c   d   0   0   0  a2 0  0 |
|d 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |  {3} | a   b   -c  -d  0  0  a2 0 |
|  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |  {3} | 0   0   a   b   0  0  0  a2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|0   0   0   0   0   0   0   0   0  cd2 c2d c3 0   0   0   0  0   0   0  0  0 |
|0   0   0   0   0   0   0   0   0  0   0   0  cd2 0   0   0  0   0   0  d3 0 |
|bd2 bcd bc2 0   0   0   0   0   0  0   0   0  0   cd2 c2d c3 0   0   0  0  d3|
|0   0   0   bd2 bcd b2d bc2 b2c b3 0   0   0  0   0   0   0  cd2 c2d c3 0  0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0|
| 0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c|
| 0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0|
| 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0  d  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0|
| 0  -c 0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0|
| 0  -b 0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0|
| d3 a  0  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  b|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  0  0  cd 0  0  0  d2 0  0  0  |)                                           |
|2 0  0  0  cd 0  0  0  d2 0  0  |                                            |
|  c2 0  0  0  cd 0  0  0  d2 0  |                                            |
|  0  c2 0  0  0  cd 0  0  0  d2 |                                            |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |, {4} | d  a2 0  0  0  ab |
|  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |  {4} | -c 0  a2 0  0  0  |
|  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |  {4} | -b 0  0  a2 0  0  |
|c 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |  {4} | a  0  0  0  a2 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0 |
|ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0 |
|0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2|
|0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|------------------------------+----------------------------------------------|
|                              |0                                             |
|                              |                                              |
|                              |{0, 4}                                        |
|                              |                                              |
|                              |                                              |
|                              |                                              |
|------------------------------+----------------------------------------------|
| 0  cd 0  0  0  d2 0  0  0  |)|subquotient ({5} | d2 cd bd ad c2 bc ac b2 ab |
| 0  0  cd 0  0  0  d2 0  0  | |                                              |
| 0  0  0  cd 0  0  0  d2 0  | |{0, 3}                                        |
| c2 0  0  0  cd 0  0  0  d2 | |                                              |
|                              |                                              |
|                              |                                              |
|------------------------------+----------------------------------------------|
|                              |subquotient ({4} | d  d2 cd bd ad c2 bc ac b2 |
|                              |             {4} | -c 0  0  0  0  0  0  0  0  |
|                              |             {4} | -b 0  0  0  0  0  0  0  0  |
|                              |             {4} | a  0  0  0  0  0  0  0  0  |
|                              |                                              |
|                              |{0, 2}                                        |
|------------------------------+----------------------------------------------|
|                              |subquotient ({2} | d c b a 0 0 0 -b2 -ac -bd -|
|                              |             {3} | 0 0 0 0 1 0 0 c   d   0   0|
|                              |             {3} | 0 0 0 0 0 1 0 a   b   -c  -|
|                              |             {3} | 0 0 0 0 0 0 1 0   0   a   b|
|                              |                                              |
|                              |{0, 1}                                        |
|------------------------------+----------------------------------------------|
|                              |cokernel | bc-ad b3-a2c ac2-b2d c3-bd2 a b c d|
|                              |                                              |
|                              |{0, 0}                                        |
|------------------------------+----------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a2 a b c d |, {5} | a b c d |)                                               |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|ab a2 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  d2 cd bd ad c2 bc ac b2 ab a2 0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  d2 cd bd ad c2 bc ac b2 ab a2 0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  d2 cd bd c2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 |, {2} | -b2 -ac -bd -c2 a 0 0 0 b 0 0 0 c|
|   0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 |  {3} | c   d   0   0   0 a 0 0 0 b 0 0 0|
|d  0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 |  {3} | a   b   -c  -d  0 0 a 0 0 0 b 0 0|
|   0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d |  {3} | 0   0   a   b   0 0 0 a 0 0 0 b 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| |                                                                           |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0  0  d  a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 |, {4} | d  a 0 0 0 b 0 0 0 c 0 0 0|
| 0  0  -c 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 |  {4} | -c 0 a 0 0 0 b 0 0 0 c 0 0|
| 0  0  -b 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 |  {4} | -b 0 0 a 0 0 0 b 0 0 0 c 0|
| bc b2 a  0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d |  {4} | a  0 0 0 a 0 0 0 b 0 0 0 c|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0 0 0 d 0 0 0 |)                                                            |
| c 0 0 0 d 0 0 |                                                             |
| 0 c 0 0 0 d 0 |                                                             |
| 0 0 c 0 0 0 d |                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------+                                                                 |
|           |                                                                 |
|           |                                                                 |
|           |                                                                 |
|           |                                                                 |
|           |                                                                 |
|           |                                                                 |
|-----------+                                                                 |
|           |                                                                 |
|           |                                                                 |
|           |                                                                 |
|           |                                                                 |
|           |                                                                 |
|           |                                                                 |
|-----------+                                                                 |
| d 0 0 0 |)|                                                                 |
| 0 d 0 0 | |                                                                 |
| 0 0 d 0 | |                                                                 |
| 0 0 0 d | |                                                                 |
|           |                                                                 |
|           |                                                                 |
|-----------+                                                                 |
|           |                                                                 |
|           |                                                                 |
|           |                                                                 |
|           |                                                                 |
|           |                                                                 |
|           |                                                                 |
|-----------+                                                                 |
|           |                                                                 |
|           |                                                                 |
|           |                                                                 |
|-----------+                                                                 |
+-----------------------------------------------------------------------------+
|i7 : prune E^3                                                               |
|                                                                             |
|     +-----------------------------------------------------------------------|
|o7 = |cokernel {4} | -d -b -d -c 0  0  -c 0  0  0  -d 0  0  0  0  -d -c 0  0 |
|     |         {4} | c  a  0  0  0  -d 0  -b 0  -d 0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  b  a  c  0  0  0  -d 0  0  -d 0  -d 0  0  0  0  0 |
|     |         {4} | 0  0  0  0  -d c  b  a  0  0  0  0  -d 0  -d 0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  c  b  a  0  0  0  0  0  0  0  -d|
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  b  a  0  0  0  0  c  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  d  c  b  a  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -d c |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |                                                                       |
|     |{-4, 4}                                                                |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 3}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 2}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 1}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 0}                                                                |
|     +-----------------------------------------------------------------------|
|                                                                             |
|o7 : SpectralSequencePage                                                    |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  -d 0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  -d 0  0  0  -d 0  0  0  0  -d 0  0  0  0  -d 0  0  0  0  0  0  0|
| -d 0  0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  -d 0  0  0  0  -d 0  0  0|
| 0  0  -d 0  0  -d 0  0  0  0  0  -d 0  0  0  0  -d 0  0  0  0  0  0  0  0  -|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| b  a  0  0  0  0  -d 0  0  0  0  0  -d 0  0  0  0  0  0  0  0  -d 0  0  0  0|
| 0  0  c  b  a  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  -d 0  0  0  0  0|
| 0  0  0  0  0  b  a  0  0  0  0  0  0  0  0  0  0  0  0  c  0  0  0  -d 0  0|
| 0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -d c  b  a  0  -d 0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  d  c  b|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|d 0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  -d 0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  -d 0  0  0  -d 0  0  0  0  0  0  -d 0  0  0  -d 0  0  -d 0  0  0  0  -d |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  -d 0  0  0  0  |
|  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  c  b  a  -d 0  0  0  -d 0  0  0  0  0  0  -d 0  0  0  0  0  0  0  -d 0  |
|  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  c  b  a  -d 0  0  0  0  0  0  -d 0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  c  b  a  -d 0  0  -d 0  0  0  0  -d 0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  0  0  0  0  -d 0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  d  c  b  a  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|----------------------------+------------------------------------------------|
|0  0  0  0  0  0  0  0  0  ||0                                               |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||{-3, 4}                                         |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  -d 0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  -d 0  0  0  -d 0  0  0  ||                                                |
|0  0  0  0  -d 0  0  0  -d ||                                                |
|-d 0  0  0  0  0  0  -d 0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|0  0  0  0  0  0  0  0  0  ||                                                |
|c  b  a  -d 0  0  0  0  0  ||                                                |
|0  0  0  c  b  a  -d 0  0  ||                                                |
|0  0  0  0  0  0  c  b  a  ||                                                |
|                            |                                                |
|                            |                                                |
|----------------------------+------------------------------------------------|
|                            |cokernel {3} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                            |         {3} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0|
|                            |         {3} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0|
|                            |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0|
|                            |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d|
|                            |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                            |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                            |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                            |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                            |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                            |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                            |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                            |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                            |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                            |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                            |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                            |                                                |
|                            |{-3, 3}                                         |
|----------------------------+------------------------------------------------|
|                            |0                                               |
|                            |                                                |
|                            |{-3, 2}                                         |
|                            |                                                |
|                            |                                                |
|                            |                                                |
|                            |                                                |
|                            |                                                |
|                            |                                                |
|                            |                                                |
|                            |                                                |
|----------------------------+------------------------------------------------|
|                            |0                                               |
|                            |                                                |
|                            |{-3, 1}                                         |
|                            |                                                |
|                            |                                                |
|                            |                                                |
|----------------------------+------------------------------------------------|
|                            |0                                               |
|                            |                                                |
|                            |{-3, 0}                                         |
|----------------------------+------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-------------------+---------------------------------------------------------|
|                   |0                                                        |
|                   |                                                         |
|                   |{-2, 4}                                                  |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|-------------------+---------------------------------------------------------|
|0 0 0 0 0 0 0 0 0 ||0                                                        |
|0 0 0 0 0 0 0 0 0 ||                                                         |
|0 0 0 0 0 0 0 0 0 ||{-2, 3}                                                  |
|0 0 0 0 0 0 0 0 0 ||                                                         |
|0 0 0 0 0 0 0 0 0 ||                                                         |
|0 0 0 0 0 0 0 0 0 ||                                                         |
|0 0 0 0 0 0 0 0 0 ||                                                         |
|0 0 0 0 0 0 0 0 0 ||                                                         |
|0 0 0 0 0 0 0 0 0 ||                                                         |
|0 0 0 0 0 0 0 0 0 ||                                                         |
|0 0 0 0 0 0 0 0 0 ||                                                         |
|0 0 0 0 0 0 0 0 0 ||                                                         |
|0 0 0 0 0 0 0 0 0 ||                                                         |
|a 0 0 0 0 0 0 0 0 ||                                                         |
|0 d c b a 0 0 0 0 ||                                                         |
|0 0 0 0 0 d c b a ||                                                         |
|                   |                                                         |
|                   |                                                         |
|-------------------+---------------------------------------------------------|
|                   |cokernel {2} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|                   |         {2} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|                   |         {2} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 |
|                   |         {2} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 |
|                   |         {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 |
|                   |         {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d |
|                   |         {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|                   |         {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|                   |         {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|                   |                                                         |
|                   |{-2, 2}                                                  |
|-------------------+---------------------------------------------------------|
|                   |0                                                        |
|                   |                                                         |
|                   |{-2, 1}                                                  |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|-------------------+---------------------------------------------------------|
|                   |0                                                        |
|                   |                                                         |
|                   |{-2, 0}                                                  |
|-------------------+---------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-------------------------------+---------------------------------------------|
|                               |0                                            |
|                               |                                             |
|                               |{-1, 4}                                      |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|-------------------------------+---------------------------------------------|
|                               |0                                            |
|                               |                                             |
|                               |{-1, 3}                                      |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|                               |                                             |
|-------------------------------+---------------------------------------------|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||cokernel {4} | d c b a 0 0 0 0 0 0 0 0 0 0 0 |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||         {4} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||         {4} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||         {4} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||         {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|c b a 0 0 0 0 0 0 0 0 0 0 0 0 ||         {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|0 0 0 d c b a 0 0 0 0 0 0 0 0 ||         {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|0 0 0 0 0 0 0 d c b a 0 0 0 0 ||         {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|0 0 0 0 0 0 0 0 0 0 0 d c b a ||                                             |
|                               |{-1, 2}                                      |
|                               |                                             |
|-------------------------------+---------------------------------------------|
|                               |cokernel {1} | d c b a 0 0 0 0 0 0 0 0 0 0 0 |
|                               |         {1} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 |
|                               |         {1} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 |
|                               |         {1} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b |
|                               |                                             |
|                               |{-1, 1}                                      |
|-------------------------------+---------------------------------------------|
|                               |0                                            |
|                               |                                             |
|                               |{-1, 0}                                      |
|-------------------------------+---------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------+----------------------------------------+|
|                                   |0                                       ||
|                                   |                                        ||
|                                   |{0, 4}                                  ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|-----------------------------------+----------------------------------------+|
|                                   |0                                       ||
|                                   |                                        ||
|                                   |{0, 3}                                  ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|-----------------------------------+----------------------------------------+|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||0                                       ||
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                                        ||
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||{0, 2}                                  ||
|a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                                        ||
|0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 ||                                        ||
|0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 ||                                        ||
|0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 ||                                        ||
|0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a ||                                        ||
|                                   |                                        ||
|                                   |                                        ||
|                                   |                                        ||
|-----------------------------------+----------------------------------------+|
|0 |                                |cokernel {3} | d c b a 0 0 0 0 0 0 0 0 |||
|0 |                                |         {3} | 0 0 0 0 d c b a 0 0 0 0 |||
|0 |                                |         {3} | 0 0 0 0 0 0 0 0 d c b a |||
|a |                                |                                        ||
|                                   |{0, 1}                                  ||
|                                   |                                        ||
|-----------------------------------+----------------------------------------+|
|                                   |cokernel | d c b a |                    ||
|                                   |                                        ||
|                                   |{0, 0}                                  ||
|-----------------------------------+----------------------------------------+|
+-----------------------------------------------------------------------------+

See also
========

  * minimalPresentation(SpectralSequence)
    -- a minimal presentation of a
    spectral sequence
  * prune(SpectralSequence),
    -- a minimal presentation of a spectral sequence
  * minimalPresentation (Macaulay2Doc) -- compute a
    minimal presentation
  * prune (Macaulay2Doc) -- prune, e.g., compute a minimal
    presentation

Ways to use this method:
========================

  * minimalPresentation(SpectralSequencePage)
    -- a minimal presentation of
    a spectral sequence page
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:3165:0.

net(FilteredComplex)
********************

  * Function: net (Macaulay2Doc),

Ways to use this method:
========================

  * net(FilteredComplex)
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2342:0.

net(Page)
*********

  * Function: net (Macaulay2Doc),

Ways to use this method:
========================

  * net(Page)
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2336:0.

net(PageMap)
************

  * Function: net (Macaulay2Doc),

Ways to use this method:
========================

  * net(PageMap)
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2331:0.

net(SpectralSequence)
*********************

  * Function: net (Macaulay2Doc),

Ways to use this method:
========================

  * net(SpectralSequence)
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2319:0.

net(SpectralSequencePage)
*************************

  * Function: net (Macaulay2Doc),

Ways to use this method:
========================

  * net(SpectralSequencePage)
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2325:0.

netPage -- display a small portion of a given Spectral Sequence page
********************************************************************

  * Usage:
        E' = netPage(E,L1,L2)
  * Inputs:
      * E, a Page,
      * L1, a list (Macaulay2Doc),
      * L2, a list (Macaulay2Doc),
  * Outputs:
      * E', a net (Macaulay2Doc),

Description
===========

Produces the portion of a given spectral sequence page that lies in the square
with given bottom right and top left coordinates.

+------------------------------------+
|i1 : R = QQ[x];                     |
+------------------------------------+
|i2 : S = R/ideal"x2";               |
+------------------------------------+
|i3 : N = S^1/ideal"x";              |
+------------------------------------+
|i4 : M = R^1/R_0;                   |
+------------------------------------+
|i5 : C = res M;                     |
+------------------------------------+
|i6 : C' = C ** S;                   |
+------------------------------------+
|i7 : D = res(N,LengthLimit => 10);  |
+------------------------------------+
|i8 : E0 = C' ** (filteredComplex D);|
+------------------------------------+
|i9 : E = prune spectralSequence E0; |
+------------------------------------+

The E_2 page has nonzero E_2^{p,q} when 0 <= p <= 10 and 0 <= q <= 1, so we may
ask to restrict the display to 2 <= p <= 6 and 0 <= q <= 1.

netPage(E_2,{2,0},{6,1})

If we ask for a square that is too large, only the relevant portion of the page
will be displayed.

+-----------------------------------------------------------------------------+
|i10 : R = QQ[x];                                                             |
+-----------------------------------------------------------------------------+
|i11 : S = R/ideal"x2";                                                       |
+-----------------------------------------------------------------------------+
|i12 : N = S^1/ideal"x";                                                      |
+-----------------------------------------------------------------------------+
|i13 : M = R^1/R_0;                                                           |
+-----------------------------------------------------------------------------+
|i14 : C = res M;                                                             |
+-----------------------------------------------------------------------------+
|i15 : C' = C ** S;                                                           |
+-----------------------------------------------------------------------------+
|i16 : D = res(N,LengthLimit => 10);                                          |
+-----------------------------------------------------------------------------+
|i17 : E0 = C' ** (filteredComplex D);                                        |
+-----------------------------------------------------------------------------+
|i18 : E = prune spectralSequence E0;                                         |
+-----------------------------------------------------------------------------+
|i19 : netPage(E_2,{-5,0},{7,1})                                              |
|                                                                             |
|      +------------------+------------------+------------------+-------------|
|o19 = |cokernel {2} | x ||cokernel {3} | x ||cokernel {4} | x ||cokernel {5} |
|      |                  |                  |                  |             |
|      |{0, 1}            |{1, 1}            |{2, 1}            |{3, 1}       |
|      +------------------+------------------+------------------+-------------|
|      |cokernel | x |    |cokernel {1} | x ||cokernel {2} | x ||cokernel {3} |
|      |                  |                  |                  |             |
|      |{0, 0}            |{1, 0}            |{2, 0}            |{3, 0}       |
|      +------------------+------------------+------------------+-------------|
|-----------------------------------------------------------------------------|
|-----+------------------+------------------+------------------+--------------|
|| x ||cokernel {6} | x ||cokernel {7} | x ||cokernel {8} | x ||cokernel {9} ||
|     |                  |                  |                  |              |
|     |{4, 1}            |{5, 1}            |{6, 1}            |{7, 1}        |
|-----+------------------+------------------+------------------+--------------|
|| x ||cokernel {4} | x ||cokernel {5} | x ||cokernel {6} | x ||cokernel {7} ||
|     |                  |                  |                  |              |
|     |{4, 0}            |{5, 0}            |{6, 0}            |{7, 0}        |
|-----+------------------+------------------+------------------+--------------|
|-----------------------------------------------------------------------------|
|----+                                                                        |
| x ||                                                                        |
|    |                                                                        |
|    |                                                                        |
|----+                                                                        |
| x ||                                                                        |
|    |                                                                        |
|    |                                                                        |
|----+                                                                        |
+-----------------------------------------------------------------------------+

Ways to use netPage:
====================

  * "netPage(Page,List,List)"

For the programmer
==================

The object netPage, is a method function (Macaulay2Doc).

-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:3331:0.

new Page
********

Ways to use this method:
========================

  * new Page
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2488:0.

Page -- the type of all pages
*****************************

Description
===========

A page is a collection of modules which are indexed by lists of integers.  This
is a parent class for the type SpectralSequencePage.
The infinity page of a spectral sequence is an example
of a page which is not a spectral sequence page.

As a specific example consider the filtered complex $K$ below, obtained by
multiplying the minimal free resolution of the rational quartic space curve by
successive powers of the irrelevant ideal.

+----------------------------------------------------+
|i1 : B = QQ[a..d];                                  |
+----------------------------------------------------+
|i2 : J = ideal vars B;                              |
|                                                    |
|o2 : Ideal of B                                     |
+----------------------------------------------------+
|i3 : C = complete res monomialCurveIdeal(B,{1,3,4});|
+----------------------------------------------------+
|i4 : K = filteredComplex(J,C,4);                    |
+----------------------------------------------------+

The infinity page of the resulting spectral sequence is computed below.

+-----------------------------------------------------------------------------+
|i5 : E = prune spectralSequence K;                                           |
+-----------------------------------------------------------------------------+
|i6 : E^infinity                                                              |
|                                                                             |
|     +-----------------------------------------------------------------------|
|o6 = |cokernel {4} | -d -b 0  -c 0  0  -d -c 0  0  0  0  0  -d 0  0  0  0  0 |
|     |         {4} | c  a  -d 0  -b 0  0  0  0  -d 0  0  -d 0  0  0  0  0  0 |
|     |         {4} | 0  0  c  b  a  -d 0  0  -d 0  0  0  0  0  0  0  -d 0  0 |
|     |         {4} | 0  0  0  0  0  c  b  a  0  0  0  -d 0  0  0  -d 0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  b  a  c  0  0  0  -d 0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  -d c  b  a  0  0  0  0  -d|
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  -d 0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |         {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|     |                                                                       |
|     |{-4, 4}                                                                |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 3}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 2}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 1}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 0}                                                                |
|     +-----------------------------------------------------------------------|
|                                                                             |
|o6 : Page                                                                    |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
| a  -d 0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0|
| 0  c  b  a  -d 0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0|
| 0  0  0  0  c  b  a  -d 0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0|
| 0  0  0  0  0  0  0  c  b  a  -d 0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  c  b  a  -d 0  0  0  0  0  0  -d 0  0  0  -d 0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  -d 0  0  0  0  0  0  -d 0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  -d 0  0  0  0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  -d 0  0  0|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  -|
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|---------+-------------------------------------------------------------------|
|  0  0  ||0                                                                  |
|  0  0  ||                                                                   |
|  0  0  ||{-3, 4}                                                            |
|  0  0  ||                                                                   |
|  0  0  ||                                                                   |
|  0  0  ||                                                                   |
|  0  0  ||                                                                   |
|  0  0  ||                                                                   |
|  0  0  ||                                                                   |
|  0  0  ||                                                                   |
|  0  0  ||                                                                   |
|  0  0  ||                                                                   |
|  0  -d ||                                                                   |
|  -d 0  ||                                                                   |
|  0  0  ||                                                                   |
|d 0  0  ||                                                                   |
|  b  a  ||                                                                   |
|         |                                                                   |
|         |                                                                   |
|---------+-------------------------------------------------------------------|
|         |cokernel {3} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|         |         {3} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|         |         {3} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|         |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 |
|         |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 |
|         |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 |
|         |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c |
|         |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|         |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|         |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|         |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|         |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|         |         {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|         |                                                                   |
|         |{-3, 3}                                                            |
|---------+-------------------------------------------------------------------|
|         |0                                                                  |
|         |                                                                   |
|         |{-3, 2}                                                            |
|         |                                                                   |
|         |                                                                   |
|         |                                                                   |
|         |                                                                   |
|         |                                                                   |
|         |                                                                   |
|         |                                                                   |
|         |                                                                   |
|---------+-------------------------------------------------------------------|
|         |0                                                                  |
|         |                                                                   |
|         |{-3, 1}                                                            |
|         |                                                                   |
|         |                                                                   |
|         |                                                                   |
|---------+-------------------------------------------------------------------|
|         |0                                                                  |
|         |                                                                   |
|         |{-3, 0}                                                            |
|---------+-------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------+-----------------------|
|                                                     |0                      |
|                                                     |                       |
|                                                     |{-2, 4}                |
|                                                     |                       |
|                                                     |                       |
|                                                     |                       |
|                                                     |                       |
|                                                     |                       |
|                                                     |                       |
|                                                     |                       |
|                                                     |                       |
|                                                     |                       |
|                                                     |                       |
|                                                     |                       |
|                                                     |                       |
|                                                     |                       |
|                                                     |                       |
|                                                     |                       |
|                                                     |                       |
|-----------------------------------------------------+-----------------------|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||0                      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                       |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||{-2, 3}                |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                       |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                       |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                       |
|b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                       |
|0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                       |
|0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||                       |
|0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 ||                       |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 ||                       |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 ||                       |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a ||                       |
|                                                     |                       |
|                                                     |                       |
|-----------------------------------------------------+-----------------------|
|                                                     |cokernel {2} | d c b a |
|                                                     |         {2} | 0 0 0 0 |
|                                                     |         {2} | 0 0 0 0 |
|                                                     |         {2} | 0 0 0 0 |
|                                                     |         {2} | 0 0 0 0 |
|                                                     |         {2} | 0 0 0 0 |
|                                                     |         {2} | 0 0 0 0 |
|                                                     |         {2} | 0 0 0 0 |
|                                                     |         {2} | 0 0 0 0 |
|                                                     |                       |
|                                                     |{-2, 2}                |
|-----------------------------------------------------+-----------------------|
|                                                     |0                      |
|                                                     |                       |
|                                                     |{-2, 1}                |
|                                                     |                       |
|                                                     |                       |
|                                                     |                       |
|-----------------------------------------------------+-----------------------|
|                                                     |0                      |
|                                                     |                       |
|                                                     |{-2, 0}                |
|-----------------------------------------------------+-----------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------+-----------|
|                                                                 |0          |
|                                                                 |           |
|                                                                 |{-1, 4}    |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|-----------------------------------------------------------------+-----------|
|                                                                 |0          |
|                                                                 |           |
|                                                                 |{-1, 3}    |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|                                                                 |           |
|-----------------------------------------------------------------+-----------|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||0          |
|d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||           |
|0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||{-1, 2}    |
|0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||           |
|0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ||           |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 ||           |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 ||           |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 ||           |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a ||           |
|                                                                 |           |
|                                                                 |           |
|-----------------------------------------------------------------+-----------|
|                                                                 |cokernel {1|
|                                                                 |         {1|
|                                                                 |         {1|
|                                                                 |         {1|
|                                                                 |           |
|                                                                 |{-1, 1}    |
|-----------------------------------------------------------------+-----------|
|                                                                 |0          |
|                                                                 |           |
|                                                                 |{-1, 0}    |
|-----------------------------------------------------------------+-----------|
|-----------------------------------------------------------------------------|
|-------------------------------------+--------------------+                  |
|                                     |0                   |                  |
|                                     |                    |                  |
|                                     |{0, 4}              |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|-------------------------------------+--------------------+                  |
|                                     |0                   |                  |
|                                     |                    |                  |
|                                     |{0, 3}              |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|-------------------------------------+--------------------+                  |
|                                     |0                   |                  |
|                                     |                    |                  |
|                                     |{0, 2}              |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|-------------------------------------+--------------------+                  |
|} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 ||0                   |                  |
|} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 ||                    |                  |
|} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 ||{0, 1}              |                  |
|} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a ||                    |                  |
|                                     |                    |                  |
|                                     |                    |                  |
|-------------------------------------+--------------------+                  |
|                                     |cokernel | d c b a ||                  |
|                                     |                    |                  |
|                                     |{0, 0}              |                  |
|-------------------------------------+--------------------+                  |
+-----------------------------------------------------------------------------+

See also
========

  * SpectralSequencePage -- the type of all
    spectral sequence pages
  * SpectralSequence ^ InfiniteNumber,
    -- the infinity page of a spectral sequence
  * SpectralSequence _ InfiniteNumber,
    -- the infinity page of a spectral sequence

Types of Page:
==============

  * SpectralSequencePage -- the type of all
    spectral sequence pages

Functions and methods returning a Page:
=======================================

  * hilbertPolynomial(SpectralSequencePage)
    -- the Hilbert polynomial of a
    spectral sequence page
  * new Page
  * "page(List,List,Page)" -- see page,
  * page(SpectralSequencePage)

Methods that use a Page:
========================

  * degree(Page)
  * describe(Page) -- real description
  * net(Page)
  * "netPage(Page,List,List)" -- see netPage, -- display a small
    portion of a given Spectral Sequence page
  * Page _ List
  * ring(Page)
  * "spots(Page)" -- see spots, -- which spots does the given page
    has a module.
  * support(Page) -- which non-zero modules appear in
    the given page.

For the programmer
==================

The object Page, is a type (Macaulay2Doc), with
ancestor classes MutableHashTable (Macaulay2Doc), <
HashTable (Macaulay2Doc) < Thing (Macaulay2Doc).

-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2467:0.

page
****

Description
===========

adds keys to a a page.

See also
========

  * Page -- the type of all pages

Ways to use page:
=================

  * "page(List,List,Page)"
  * page(SpectralSequencePage)

For the programmer
==================

The object page, is a method function with options (Macaulay2Doc).

-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2369:0.

Page _ List
***********

  * Operator: _ (Macaulay2Doc),

Ways to use this method:
========================

  * Page _ List
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2312:0.

page(...,Prune=>...)
********************

Functions with optional argument named Prune:
=============================================

  * page(...,Prune=>...)
  * spectralSequence(...,Prune=>...)
  * spectralSequencePage(...,Prune=>...)
  * spectralSequencePageMap(...,Prune=>...)

Further information
===================

  * Default value: false (Macaulay2Doc),
  * Function: page,
  * Option key: Prune (Macaulay2Doc), -- value of an optional
    argument
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:1096:0.

page(SpectralSequencePage)
**************************

  * Function: page,

Ways to use this method:
========================

  * page(SpectralSequencePage)
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2306:0.

PageMap -- the type of all page maps
************************************

Description
===========

A page map is a collection of homomorphisms which are indexed by lists of
integers.  This is a parent class for the type SpectralSequencePageMap.
The output of the method
pruningMaps(SpectralSequencePage) is an example of a Page which is not a
SpectralSequencePage.

As a specific example consider the filtered complex $K$ below, obtained by
multiplying the minimal free resolution of the rational quartic space curve by
successive powers of the irrelevant ideal.

+----------------------------------------------------+
|i1 : B = QQ[a..d];                                  |
+----------------------------------------------------+
|i2 : J = ideal vars B;                              |
|                                                    |
|o2 : Ideal of B                                     |
+----------------------------------------------------+
|i3 : C = complete res monomialCurveIdeal(B,{1,3,4});|
+----------------------------------------------------+
|i4 : K = filteredComplex(J,C,4);                    |
+----------------------------------------------------+

We compute an example of a pruning map below.

+-----------------------------------------------------------------------------+
|i5 : E = prune spectralSequence K;                                           |
+-----------------------------------------------------------------------------+
|i6 : pruningMaps E^2                                                         |
|                                                                             |
|o6 = {-7, 6} : subquotient (| 0 a4bc-a5d a4b3-a6c a5c2-a4b2d a4c3-a4bd2 a3b2c|
|                                                                             |
|                                                                             |
|     {-7, 7} : subquotient ({2} | 0 0 0 0 -a4b2 -a5c -a4bd -a4c2 -a3b3 -a4bc |
|                            {3} | 0 0 0 0 a4c   a4d  0     0     a3bc  a3bd  |
|                            {3} | 0 0 0 0 a5    a4b  -a4c  -a4d  a4b   a3b2  |
|                            {3} | 0 0 0 0 0     0    a5    a4b   0     0     |
|                                                                             |
|     {-7, 8} : subquotient ({4} | 0 0 0 0 a4d  a3bd  a3cd  a3d2  a2b2d  a2bcd|
|                            {4} | 0 0 0 0 -a4c -a3bc -a3c2 -a3cd -a2b2c -a2bc|
|                            {4} | 0 0 0 0 -a4b -a3b2 -a3bc -a3bd -a2b3  -a2b2|
|                            {4} | 0 0 0 0 a5   a4b   a4c   a4d   a3b2   a3bc |
|                                                                             |
|     {-7, 9} : image 0 <----- 0 : {-5, 8}                                    |
|                          0                                                  |
|                                                                             |
|     {-7, 10} : 0 <----- 0 : {-5, 9}                                         |
|                     0                                                       |
|                                                                             |
|     {-2, 1} : cokernel | bc-ad b3-a2c ac2-b2d c3-bd2 a b c d | <--------- co|
|                                                                   | 1 |     |
|                                                                             |
|     {-2, 2} : cokernel {2} | -b2 -ac -bd -c2 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0|
|                        {3} | c   d   0   0   0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0|
|                        {3} | a   b   -c  -d  0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0|
|                        {3} | 0   0   a   b   0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d|
|                                                                             |
|                                                                             |
|     {-2, 3} : subquotient ({4} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 d  a 0 0 0 |
|                            {4} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 -c 0 a 0 0 |
|                            {4} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 -b 0 0 a 0 |
|                            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a a  0 0 0 a |
|                                                                             |
|     {-2, 4} : subquotient ({5} | d c b a a b c d |, {5} | a b c d |) <----- |
|                                                                         0   |
|                                                                             |
|     {-2, 5} : 0 <----- 0 : {0, 4}                                           |
|                    0                                                        |
|                                                                             |
|     {-3, 2} : subquotient (| a b c d bc-ad b3-a2c ac2-b2d c3-bd2 a2 ab ac ad|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|     {-3, 3} : subquotient ({2} | a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 -b2 -ac -bd|
|                            {3} | 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 c   d   0  |
|                            {3} | 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 a   b   -c |
|                            {3} | 0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0   0   a  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|     {-3, 4} : subquotient ({4} | d  ad ac ab a2 0  0  0  0  0  0  0  0  0  0|
|                            {4} | -c 0  0  0  0  ad ac ab a2 0  0  0  0  0  0|
|                            {4} | -b 0  0  0  0  0  0  0  0  ad ac ab a2 0  0|
|                            {4} | a  0  0  0  0  0  0  0  0  0  0  0  0  ad a|
|                                                                             |
|     {-3, 5} : subquotient ({5} | ad ac ab a2 bd bc b2 ab cd c2 bc ac d2 cd b|
|                                                                             |
|                                                                             |
|     {-3, 6} : 0 <----- 0 : {-1, 5}                                          |
|                    0                                                        |
|                                                                             |
|     {-4, 3} : subquotient (| a2 ab ac ad b2 bc bd c2 cd d2 abc-a2d ab3-a3c a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|     {-4, 4} : subquotient ({2} | a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0|
|                            {3} | 0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0|
|                            {3} | 0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  a|
|                            {3} | 0  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|     {-4, 5} : subquotient ({4} | ad  bd  cd  d2  a2d a2c a2b a3 0   0   0   |
|                            {4} | -ac -bc -c2 -cd 0   0   0   0  a2d a2c a2b |
|                            {4} | -ab -b2 -bc -bd 0   0   0   0  0   0   0   |
|                            {4} | a2  ab  ac  ad  0   0   0   0  0   0   0   |
|                                                                             |
|     {-4, 6} : subquotient ({5} | a2d a2c a2b a3 abd abc ab2 a2b acd ac2 abc |
|                                                                             |
|                                                                             |
|     {-4, 7} : 0 <----- 0 : {-2, 6}                                          |
|                    0                                                        |
|                                                                             |
|     {-5, 4} : subquotient (| a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3 b2c b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|     {-5, 5} : subquotient ({2} | 0 a2b2 a2bd a2bd 0 a3c  a3c  a2c2 a2b2 ab3 |
|                            {3} | 0 -a2c 0    0    0 -a2d -a2d 0    -a2c -abc|
|                            {3} | 0 -a3  a2c  a2c  0 -a2b -a2b a2d  -a3  -a2b|
|                            {3} | 0 0    -a3  -a3  0 0    0    -a2b 0    0   |
|                                                                             |
|     {-5, 6} : subquotient ({4} | a2d  abd  acd  ad2  b2d  bcd  bd2  c2d  cd2|
|                            {4} | -a2c -abc -ac2 -acd -b2c -bc2 -bcd -c3  -c2|
|                            {4} | -a2b -ab2 -abc -abd -b3  -b2c -b2d -bc2 -bc|
|                            {4} | a3   a2b  a2c  a2d  ab2  abc  abd  ac2  acd|
|                                                                             |
|     {-5, 7} : subquotient ({5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                                                                             |
|                                                                             |
|     {-5, 8} : 0 <----- 0 : {-3, 7}                                          |
|                    0                                                        |
|                                                                             |
|     {-6, 5} : subquotient (| a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|     {-6, 6} : subquotient ({2} | 0 a3b2 a3bd a3bd 0 a4c  a4c  a3c2 a3b2 a2b3|
|                            {3} | 0 -a3c 0    0    0 -a3d -a3d 0    -a3c -a2b|
|                            {3} | 0 -a4  a3c  a3c  0 -a3b -a3b a3d  -a4  -a3b|
|                            {3} | 0 0    -a4  -a4  0 0    0    -a3b 0    0   |
|                                                                             |
|     {-6, 7} : subquotient ({4} | a3d  a2bd  a2cd  a2d2  ab2d  abcd  abd2  ac|
|                            {4} | -a3c -a2bc -a2c2 -a2cd -ab2c -abc2 -abcd -a|
|                            {4} | -a3b -a2b2 -a2bc -a2bd -ab3  -ab2c -ab2d -a|
|                            {4} | a4   a3b   a3c   a3d   a2b2  a2bc  a2bd  a2|
|                                                                             |
|     {-6, 8} : image 0 <----- 0 : {-4, 7}                                    |
|                          0                                                  |
|                                                                             |
|     {-6, 9} : 0 <----- 0 : {-4, 8}                                          |
|                    0                                                        |
|                                                                             |
|o6 : PageMap                                                                 |
|-----------------------------------------------------------------------------|
|-a4bd a3b4-a5bc a4bc2-a3b3d a3bc3-a3b2d2 a3bc2-a4cd a3b3c-a5c2 a4c3-a3b2cd a3|
|                                                                             |
|                                                                             |
|-a3b2d -a3bc2 -a3b2c -a4c2 -a3bcd -a3c3 -a3b2d -a4cd -a3bd2 -a3c2d -a2b4 -a3b|
|0      0      a3c2   a3cd  0      0     a3cd   a3d2  0      0      a2b2c a2b2|
|-a3bc  -a3bd  a4c    a3bc  -a3c2  -a3cd a4d    a3bd  -a3cd  -a3d2  a3b2  a2b3|
|a4b    a3b2   0      0     a4c    a3bc  0      0     a4d    a3bd   0     0   |
|                                                                             |
|  a2bd2  a2c2d  a2cd2  a2d3   ab3d  ab2cd  ab2d2  abc2d  abcd2  abd3   ac3d  |
|2 -a2bcd -a2c3  -a2c2d -a2cd2 -ab3c -ab2c2 -ab2cd -abc3  -abc2d -abcd2 -ac4  |
|c -a2b2d -a2bc2 -a2bcd -a2bd2 -ab4  -ab3c  -ab3d  -ab2c2 -ab2cd -ab2d2 -abc3 |
|  a3bd   a3c2   a3cd   a3d2   a2b3  a2b2c  a2b2d  a2bc2  a2bcd  a2bd2  a2c3  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|kernel | d c b a | : {0, 0}                                                  |
|                                                                             |
|                                                                             |
| | <------------------- cokernel {2} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 | : {0|
| |    {2} | 1 0 0 0 |            {3} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 |     |
| |    {3} | 0 1 0 0 |            {3} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 |     |
| |    {3} | 0 0 1 0 |            {3} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a |     |
|      {3} | 0 0 0 1 |                                                        |
|                                                                             |
|b 0 0 0 c 0 0 0 d 0 0 0 |, {4} | d  a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 |) <-----|
|0 b 0 0 0 c 0 0 0 d 0 0 |  {4} | -c 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 |     0  |
|0 0 b 0 0 0 c 0 0 0 d 0 |  {4} | -b 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 |        |
|0 0 0 b 0 0 0 c 0 0 0 d |  {4} | a  0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d |        |
|                                                                             |
|0 : {0, 3}                                                                   |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| b2 bc bd c2 cd d2 |, | bc-ad b3-a2c ac2-b2d c3-bd2 a2 ab ac ad b2 bc bd c2 c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| -c2 a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  |
| 0   0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  |
| -d  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  |
| b   0  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|  0  0  bd bc b2 ab 0  0  0  0  0  0  0  0  0  0  0  0  cd c2 bc ac 0  0  0  |
|  0  0  0  0  0  0  bd bc b2 ab 0  0  0  0  0  0  0  0  0  0  0  0  cd c2 bc |
|  0  0  0  0  0  0  0  0  0  0  bd bc b2 ab 0  0  0  0  0  0  0  0  0  0  0  |
|c ab a2 0  0  0  0  0  0  0  0  0  0  0  0  bd bc b2 ab 0  0  0  0  0  0  0  |
|                                                                             |
|d ad a2 ab ac ad b2 bc bd c2 cd d2 |, {5} | a2 ab ac ad b2 bc bd c2 cd d2 |) |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2c2-ab2d ac3-abd2 b2c-abd b4-a2bc abc2-b3d bc3-b2d2 bc2-acd b3c-a2c2 ac3-b2cd|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |
|  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |
|d 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |
|  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0  0   0   0   0  0   0   0   0  abd abc ab2 a2b 0   0   0   0   0   0   0   |
|a3 0   0   0   0  0   0   0   0  0   0   0   0   abd abc ab2 a2b 0   0   0   |
|0  a2d a2c a2b a3 0   0   0   0  0   0   0   0   0   0   0   0   abd abc ab2 |
|0  0   0   0   0  a2d a2c a2b a3 0   0   0   0   0   0   0   0   0   0   0   |
|                                                                             |
|a2c ad2 acd abd a2d b2d b2c b3 ab2 bcd bc2 b2c abc bd2 bcd b2d abd c2d c3 bc2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2d bc2 bcd bd2 c3 c2d cd2 d3 a2bc-a3d a2b3-a4c a3c2-a2b2d a2c3-a2bd2 ab2c-a2b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| ab2d ab2d a2bd a2bc a2bc a2bc abc2 abc2 a2c2 ab2c ab2c abcd abcd abcd 0     |
| 0    0    0    -abd -abd -abd 0    0    0    -ac2 -ac2 0    0    0    acd   |
| abc  abc  a2c  -ab2 -ab2 -ab2 abd  abd  a2d  -a2c -a2c ac2  ac2  ac2  abc+a2|
| -a2b -a2b -a3  0    0    0    -ab2 -ab2 -a2b 0    0    -a2c -a2c -a2c -a2b  |
|                                                                             |
|  d3   a3d  0 0 -a2bd 0 0 0 0 -a2cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -ab2d -|
|d -cd2 -a3c 0 0 a2bc  0 0 0 0 a2c2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ab2c  a|
|d -bd2 -a3b 0 0 a2b2  0 0 0 0 a2bc  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ab3   a|
|  ad2  a4   0 0 -a3b  0 0 0 0 -a3c  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a2b2 -|
|                                                                             |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a4 a3b a3c a3d a2b2 a2bc a2bd |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|3 ab2c ab2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|  a2b2d a2b2d a3bd a3bc  a3bc  a3bc  a2bc2 a2bc2 a3c2 a2b2c a2b2c a2bcd a2bcd|
|c 0     0     0    -a2bd -a2bd -a2bd 0     0     0    -a2c2 -a2c2 0     0    |
|  a2bc  a2bc  a3c  -a2b2 -a2b2 -a2b2 a2bd  a2bd  a3d  -a3c  -a3c  a2c2  a2c2 |
|  -a3b  -a3b  -a4  0     0     0     -a2b2 -a2b2 -a3b 0     0     -a3c  -a3c |
|                                                                             |
|2d  acd2  ad3   b3d  b2cd  b2d2  bc2d  bcd2  bd3   c3d  c2d2  cd3   d4   a4d |
|c3  -ac2d -acd2 -b3c -b2c2 -b2cd -bc3  -bc2d -bcd2 -c4  -c3d  -c2d2 -cd3 -a4c|
|bc2 -abcd -abd2 -b4  -b3c  -b3d  -b2c2 -b2cd -b2d2 -bc3 -bc2d -bcd2 -bd3 -a4b|
|c2  a2cd  a2d2  ab3  ab2c  ab2d  abc2  abcd  abd2  ac3  ac2d  acd2  ad3  a5  |
|-----------------------------------------------------------------------------|
|c4-a3bcd2 a3bcd-a4d2 a3b3d-a5cd a4c2d-a3b2d2 a3c3d-a3bd3 a2b3c-a3b2d a2b5-a4b|
|                                                                             |
|                                                                             |
|2c -a2b3d -a2b2c2 -a2b3c -a3bc2 -a2b2cd -a2bc3 -a2b3d -a3bcd -a2b2d2 -a2bc2d |
|d  0      0       a2bc2  a2bcd  0       0      a2bcd  a2bd2  0       0       |
|   -a2b2c -a2b2d  a3bc   a2b2c  -a2bc2  -a2bcd a3bd   a2b2d  -a2bcd  -a2bd2  |
|   a3b2   a2b3    0      0      a3bc    a2b2c  0      0      a3bd    a2b2d   |
|                                                                             |
|ac2d2  acd3   ad4   b4d  b3cd  b3d2  b2c2d b2cd2  b2d3   bc3d  bc2d2  bcd3   |
|-ac3d  -ac2d2 -acd3 -b4c -b3c2 -b3cd -b2c3 -b2c2d -b2cd2 -bc4  -bc3d  -bc2d2 |
|-abc2d -abcd2 -abd3 -b5  -b4c  -b4d  -b3c2 -b3cd  -b3d2  -b2c3 -b2c2d -b2cd2 |
|a2c2d  a2cd2  a2d3  ab4  ab3c  ab3d  ab2c2 ab2cd  ab2d2  abc3  abc2d  abcd2  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|, 1}                                                                         |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0 : {0, 2}                                                                  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|d d2 |) <------------------- cokernel {1} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 ||
|           {1} | 1 0 0 0 |            {1} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 ||
|           {1} | 0 1 0 0 |            {1} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 ||
|           {1} | 0 0 1 0 |            {1} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a ||
|           {1} | 0 0 0 1 |                                                   |
|           {2} | 0 0 0 0 |                                                   |
|           {3} | 0 0 0 0 |                                                   |
|           {3} | 0 0 0 0 |                                                   |
|           {3} | 0 0 0 0 |                                                   |
|           {2} | 0 0 0 0 |                                                   |
|           {2} | 0 0 0 0 |                                                   |
|           {2} | 0 0 0 0 |                                                   |
|           {2} | 0 0 0 0 |                                                   |
|           {2} | 0 0 0 0 |                                                   |
|           {2} | 0 0 0 0 |                                                   |
|           {2} | 0 0 0 0 |                                                   |
|           {2} | 0 0 0 0 |                                                   |
|           {2} | 0 0 0 0 |                                                   |
|           {2} | 0 0 0 0 |                                                   |
|                                                                             |
|bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |, {2} | -b2 -ac -bd -c2 a2 0|
|0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |  {3} | c   d   0   0   0  a|
|0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |  {3} | a   b   -c  -d  0  0|
|0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |  {3} | 0   0   a   b   0  0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  d  a2 0  0  0 |
|ac 0  0  0  0  0  0  0  0  d2 cd bd ad 0  0  0  0  0  0  0  0  -c 0  a2 0  0 |
|0  cd c2 bc ac 0  0  0  0  0  0  0  0  d2 cd bd ad 0  0  0  0  -b 0  0  a2 0 |
|0  0  0  0  0  cd c2 bc ac 0  0  0  0  0  0  0  0  d2 cd bd ad a  0  0  0  a2|
|                                                                             |
|<----- 0 : {-1, 4}                                                           |
|   0                                                                         |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| c4-bcd2 bcd-ad2 b3d-a2cd ac2d-b2d2 c3d-bd3 a3 a2b a2c a2d ab2 abc abd ac2 ac|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-ab2 -a2c -abd -ac2 -b3 -abc -b2d -bc2 -b2c -ac2 -bcd -c3 -b2d -acd -bd2 -c2d|
|ac   ad   0    0    bc  bd   0    0    c2   cd   0    0   cd   d2   0    0   |
|a2   ab   -ac  -ad  ab  b2   -bc  -bd  ac   bc   -c2  -cd ad   bd   -cd  -d2 |
|0    0    a2   ab   0   0    ab   b2   0    0    ac   bc  0    0    ad   bd  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0   0   0   0   0   acd ac2 abc a2c 0   0   0   0   0   0   0   0   0   0   0|
|0   0   0   0   0   0   0   0   0   acd ac2 abc a2c 0   0   0   0   0   0   0|
|a2b 0   0   0   0   0   0   0   0   0   0   0   0   acd ac2 abc a2c 0   0   0|
|0   abd abc ab2 a2b 0   0   0   0   0   0   0   0   0   0   0   0   acd ac2 a|
|                                                                             |
| ac2 cd2 c2d bcd acd d3 cd2 bd2 ad2 a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|d ab4-a3bc a2bc2-ab3d abc3-ab2d2 abc2-a2cd ab3c-a3c2 a2c3-ab2cd ac4-abcd2 abc|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|  abd2 ac3  abd2 0 a2cd a2cd a2cd ac2d ac2d ab3  ab2c b4   b3d  b3d  ab2d 0  |
|  0    0    0    0 -ad2 -ad2 -ad2 0    0    -abc -ac2 -b2c 0    0    0    -ac|
|d acd  acd  acd  0 -abd -abd -abd ad2  ad2  -a2b -a2c -ab2 b2c  b2c  abc  b3-|
|  -a2d -abc -a2d 0 0    0    0    -abd -abd 0    0    0    -ab2 -ab2 -a2b 0  |
|                                                                             |
|a2bd 0 0 0 -abcd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -ac2d -abcd -a2cd 0 0 0 0 |
|2bc  0 0 0 abc2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ac3   abc2  a2c2  0 0 0 0 |
|2b2  0 0 0 ab2c  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 abc2  ab2c  a2bc  0 0 0 0 |
|a3b  0 0 0 -a2bc 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a2c2 -a2bc -a3c  0 0 0 0 |
|                                                                             |
|a2c2 a2cd a2d2 ab3 ab2c ab2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2d bcd2 bd3 c4 c3d c2d2 cd3 d4 a3bc-a4d a3b3-a5c a4c2-a3b2d a3c3-a3bd2 a2b2c-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| a2bcd 0        a2bd2 a2c3  a2bd2 0 a3cd  a3cd  a3cd  a2c2d a2c2d a2b3  a2b2c|
| 0     a2cd     0     0     0     0 -a2d2 -a2d2 -a2d2 0     0     -a2bc -a2c2|
| a2c2  a2bc+a3d a2cd  a2cd  a2cd  0 -a2bd -a2bd -a2bd a2d2  a2d2  -a3b  -a3c |
| -a3c  -a3b     -a3d  -a2bc -a3d  0 0     0     0     -a2bd -a2bd 0     0    |
|                                                                             |
| 0 0 -a3bd 0 0 0 0 -a3cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a2b2d -a3bd 0 0 0|
| 0 0 a3bc  0 0 0 0 a3c2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a2b2c  a3bc  0 0 0|
| 0 0 a3b2  0 0 0 0 a3bc  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a2b3   a3b2  0 0 0|
| 0 0 -a4b  0 0 0 0 -a4c  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a3b2  -a4b  0 0 0|
|-----------------------------------------------------------------------------|
|2c a3b2c2-a2b4d a2b2c3-a2b3d2 a2b2c2-a3bcd a2b4c-a4bc2 a3bc3-a2b3cd a2bc4-a2b|
|                                                                             |
|                                                                             |
|-a2b2c2 -a3c3 -a2bc2d -a2c4  -a2b2cd -a3c2d -a2bcd2 -a2c3d -a2b2d2 -a3cd2 -a2|
|a2c3    a2c2d 0       0      a2c2d   a2cd2  0       0      a2cd2   a2d3   0  |
|a3c2    a2bc2 -a2c3   -a2c2d a3cd    a2bcd  -a2c2d  -a2cd2 a3d2    a2bd2  -a2|
|0       0     a3c2    a2bc2  0       0      a3cd    a2bcd  0       0      a3d|
|                                                                             |
|bd4   c4d  c3d2  c2d3   cd4   d5   0 0 0 0 |, {4} | a4d  a3bd  a3cd  a3d2  a2|
|-bcd3 -c5  -c4d  -c3d2  -c2d3 -cd4 0 0 0 0 |  {4} | -a4c -a3bc -a3c2 -a3cd -a|
|-b2d3 -bc4 -bc3d -bc2d2 -bcd3 -bd4 0 0 0 0 |  {4} | -a4b -a3b2 -a3bc -a3bd -a|
|abd3  ac4  ac3d  ac2d2  acd3  ad4  0 0 0 0 |  {4} | a5   a4b   a4c   a4d   a3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| : {-1, 1}                                                                   |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  |
|2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  |
|  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd |
|  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0|
| 0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c|
| 0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0|
| 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|d ad2 b3 b2c b2d bc2 bcd bd2 c3 c2d cd2 d3 |, | abc-a2d ab3-a3c a2c2-ab2d ac3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   |
| 0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   |
| 0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   |
| 0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|   0   0   0   0   0   0   0   0   0   0   0   0   0   b2d b2c b3 ab2 0   0  |
|   0   ad2 acd abd a2d 0   0   0   0   0   0   0   0   0   0   0  0   b2d b2c|
|   0   0   0   0   0   ad2 acd abd a2d 0   0   0   0   0   0   0  0   0   0  |
|bc a2c 0   0   0   0   0   0   0   0   ad2 acd abd a2d 0   0   0  0   0   0  |
|                                                                             |
| b2c b2d bc2 bcd bd2 c3 c2d cd2 d3 |, {5} | a3 a2b a2c a2d ab2 abc abd ac2 ac|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|d-a2d2 ab3d-a3cd a2c2d-ab2d2 ac3d-abd3 b3c-ab2d b5-a2b2c ab2c2-b4d b2c3-b3d2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|      b2c2 b2c2 abc2 b3c  b3c  b2cd b2cd b2cd abcd 0       b2d2 bc3  b2d2 abd|
|2+b2d 0    0    0    -bc2 -bc2 0    0    0    0    bcd     0    0    0    0  |
|a2c   b2d  b2d  abd  -abc -abc bc2  bc2  bc2  ac2  b2c+abd bcd  bcd  bcd  acd|
|      -b3  -b3  -ab2 0    0    -abc -abc -abc -a2c -ab2    -abd -b2c -abd -a2|
|                                                                             |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -b3d -ab2d 0 0 0 -b2cd 0 0 0 0 0 0 0 |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b3c  ab2c  0 0 0 b2c2  0 0 0 0 0 0 0 |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b4   ab3   0 0 0 b3c   0 0 0 0 0 0 0 |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -ab3 -a2b2 0 0 0 -ab2c 0 0 0 0 0 0 0 |
|                                                                             |
| b2cd b2d2 bc3 bc2d bcd2 bd3 c4 c3d c2d2 cd3 d4 |, {5} | a4 a3b a3c a3d a2b2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|a3bd a2b4-a4bc a3bc2-a2b3d a2bc3-a2b2d2 a2bc2-a3cd a2b3c-a4c2 a3c3-a2b2cd a2c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| ab4   ab3d  ab3d  a2b2d 0          ab2c2 ab2c2 a2bc2 ab3c  ab3c  ab2cd ab2cd|
| -ab2c 0     0     0     -a2c2+ab2d 0     0     0     -abc2 -abc2 0     0    |
| -a2b2 ab2c  ab2c  a2bc  ab3-a3c    ab2d  ab2d  a2bd  -a2bc -a2bc abc2  abc2 |
| 0     -a2b2 -a2b2 -a3b  0          -ab3  -ab3  -a2b2 0     0     -a2bc -a2bc|
|                                                                             |
| -a2bcd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a2c2d -a2bcd -a3cd 0 0 0 0 0 0 0 0|
| a2bc2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a2c3   a2bc2  a3c2  0 0 0 0 0 0 0 0|
| a2b2c  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a2bc2  a2b2c  a3bc  0 0 0 0 0 0 0 0|
| -a3bc  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a3c2  -a3bc  -a4c  0 0 0 0 0 0 0 0|
|-----------------------------------------------------------------------------|
|2cd2 a2b2cd-a3bd2 a2b4d-a4bcd a3bc2d-a2b3d2 a2bc3d-a2b2d3 a2bc3-a3c2d a2b3c2-|
|                                                                             |
|                                                                             |
|bd3 -a2c2d2 -ab5 -a2b3c -ab4d -ab3c2 -ab4c -a2b2c2 -ab3cd -ab2c3 -ab4d -a2b2c|
|    0       ab3c ab3d   0     0      ab2c2 ab2cd   0      0      ab2cd ab2d2 |
|cd2 -a2d3   a2b3 ab4    -ab3c -ab3d  a2b2c ab3c    -ab2c2 -ab2cd a2b2d ab3d  |
|2   a2bd2   0    0      a2b3  ab4    0     0       a2b2c  ab3c   0     0     |
|                                                                             |
|b2d  a2bcd  a2bd2  a2c2d  a2cd2  a2d3   ab3d  ab2cd  ab2d2  abc2d  abcd2  abd|
|2b2c -a2bc2 -a2bcd -a2c3  -a2c2d -a2cd2 -ab3c -ab2c2 -ab2cd -abc3  -abc2d -ab|
|2b3  -a2b2c -a2b2d -a2bc2 -a2bcd -a2bd2 -ab4  -ab3c  -ab3d  -ab2c2 -ab2cd -ab|
|b2   a3bc   a3bd   a3c2   a3cd   a3d2   a2b3  a2b2c  a2b2d  a2bc2  a2bcd  a2b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |) <----------------------------------|
|0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |     {3} | 1 0 0 0 0 0  0 0 0 0  0 0 |
|0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |     {4} | 0 1 0 0 0 0  0 0 0 0  0 0 |
|bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |     {4} | 0 0 0 0 0 -1 0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  1 0 0 0  0 0 |
|                                             {3} | 0 0 1 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 1 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 -1 0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  1 0 |
|                                             {3} | 0 0 0 0 1 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 1 0 0  0 0 |
|                                             {3} | 0 0 0 0 0 0  0 0 1 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 1 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                                                             |
|  0  0  cd 0  0  0  d2 0  0  0  |, {4} | d  a2 0  0  0  ab 0  0  0  ac 0  0  |
|2 0  0  0  cd 0  0  0  d2 0  0  |  {4} | -c 0  a2 0  0  0  ab 0  0  0  ac 0  |
|  c2 0  0  0  cd 0  0  0  d2 0  |  {4} | -b 0  0  a2 0  0  0  ab 0  0  0  ac |
|  0  c2 0  0  0  cd 0  0  0  d2 |  {4} | a  0  0  0  a2 0  0  0  ab 0  0  0  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-abd2 b2c-abd b4-a2bc abc2-b3d bc3-b2d2 bc2-acd b3c-a2c2 ac3-b2cd c4-bcd2 bcd|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0|
|0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0|
|0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0|
|0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0  0   0   0   0  0   0   0   0  0   bcd bc2 b2c abc 0   0   0   0   0   0  |
| b3 ab2 0   0   0  0   0   0   0  0   0   0   0   0   bcd bc2 b2c abc 0   0  |
| 0  0   b2d b2c b3 ab2 0   0   0  0   0   0   0   0   0   0   0   0   bcd bc2|
| 0  0   0   0   0  0   b2d b2c b3 ab2 0   0   0   0   0   0   0   0   0   0  |
|                                                                             |
|d ad2 b3 b2c b2d bc2 bcd bd2 c3 c2d cd2 d3 |) <----- 0 : {-2, 5}             |
|                                                 0                           |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|b2c2-abcd b4c-a2bc2 abc3-b3cd bc4-b2cd2 b2cd-abd2 b4d-a2bcd abc2d-b3d2 bc3d-b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2 0       bc2d bc2d bc3  ac3  0       0        bc2d ac2d 0       bcd2 bcd2 c4|
|  bd2     0    0    0    0    c3      0        0    0    c2d     0    0    0 |
|  ac2+b2d bd2  bd2  bcd  acd  ac2+b2d c3-bd2   bd2  ad2  bc2+acd c2d  c2d  c2|
|d -a2c    -b2d -b2d -b2c -abc -b3     -ac2+b2d -b2d -abd -abc    -acd -acd -b|
|                                                                             |
|0 0 0 0 0 0 0 0 0 0 -bc2d -b2cd -abcd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 bc3   b2c2  abc2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 b2c2  b3c   ab2c  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 -abc2 -ab2c -a2bc 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                                                                             |
|a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|4-a2bcd2 a2bcd-a3d2 a2b3d-a4cd a3c2d-a2b2d2 a2c3d-a2bd3 ab3c-a2b2d ab5-a3b2c |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| ab2cd a2bcd 0         ab2d2 abc3  ab2d2 a2bd2 0         abc2d abc2d abc3  a2|
| 0     0     abcd      0     0     0     0     abd2      0     0     0     0 |
| abc2  a2c2  ab2c+a2bd abcd  abcd  abcd  a2cd  a2c2+ab2d abd2  abd2  abcd  a2|
| -a2bc -a3c  -a2b2     -a2bd -ab2c -a2bd -a3d  -a3c      -ab2d -ab2d -ab2c -a|
|                                                                             |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -ab3d -a2b2d 0 0 0 -ab2cd 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ab3c  a2b2c  0 0 0 ab2c2  0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ab4   a2b3   0 0 0 ab3c   0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a2b3 -a3b2  0 0 0 -a2b2c 0 0 0 0 0 0 0 0 0 |
|-----------------------------------------------------------------------------|
|a4c3 a3c4-a2b2c2d a2c5-a2bc2d2 a2bc2d-a3cd2 a2b3cd-a4c2d a3c3d-a2b2cd2 a2c4d-|
|                                                                             |
|                                                                             |
|d -ab3d2 -ab2c2d -ab3c2 -a2bc3 -ab2c2d -abc4  -ab3cd -a2bc2d -ab2cd2 -abc3d -|
|  0      0       abc3   abc2d  0       0      abc2d  abcd2   0       0      a|
|  -ab2cd -ab2d2  a2bc2  ab2c2  -abc3   -abc2d a2bcd  ab2cd   -abc2d  -abcd2 a|
|  a2b2d  ab3d    0      0      a2bc2   ab2c2  0      0       a2bcd   ab2cd  0|
|                                                                             |
|3   ac3d  ac2d2  acd3   ad4   b4d  b3cd  b3d2  b2c2d b2cd2  b2d3   bc3d  bc2d|
|cd2 -ac4  -ac3d  -ac2d2 -acd3 -b4c -b3c2 -b3cd -b2c3 -b2c2d -b2cd2 -bc4  -bc3|
|2d2 -abc3 -abc2d -abcd2 -abd3 -b5  -b4c  -b4d  -b3c2 -b3cd  -b3d2  -b2c3 -b2c|
|d2  a2c3  a2c2d  a2cd2  a2d3  ab4  ab3c  ab3d  ab2c2 ab2cd  ab2d2  abc3  abc2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|--- cokernel {3} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
||            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 |
||            {3} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
||            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 |
||            {3} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
||            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 |
||            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d |
||            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
||            {3} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 |
||            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
||            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
||            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
|                                                                             |
|0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2|
|0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0 |
|0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0 |
|ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-ad2 b3d-a2cd ac2d-b2d2 c3d-bd3 a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3 b2c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0 |
|   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0 |
|   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0 |
|d2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bc|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   c2d |
| 0   0   0   0   0   0   bd2 bcd b2d abd 0   0   0   0   0   0   0   0   0   |
| b2c abc 0   0   0   0   0   0   0   0   bd2 bcd b2d abd 0   0   0   0   0   |
| 0   0   bcd bc2 b2c abc 0   0   0   0   0   0   0   0   bd2 bcd b2d abd 0   |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2d3 bc3-ac2d b3c2-a2c3 ac4-b2c2d c5-bc2d2 bc2d-acd2 b3cd-a2c2d ac3d-b2cd2 c4d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|   bcd2 0       bd3  c3d  c3d  0 bd3  0 acd2 acd2 acd2 c2d2 c2d2 0 0 0       |
|   0    cd2     0    0    0    0 0    0 -d3  -d3  -d3  0    0    0 0 -a2cd   |
|d  c2d  bcd+ad2 cd2  cd2  cd2  0 cd2  0 -bd2 -bd2 -bd2 d3   d3   0 0 -a2bc-a3|
|c2 -acd -abd    -ad2 -bcd -bcd 0 -ad2 0 0    0    0    -bd2 -bd2 0 0 a3b     |
|                                                                             |
| 0 0 0 0 -c3d -bc2d -ac2d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
| 0 0 0 0 c4   bc3   ac3   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
| 0 0 0 0 bc3  b2c2  abc2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
| 0 0 0 0 -ac3 -abc2 -a2c2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                                                                             |
|c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 bd3 c4 c3d c2d2 cd3 d4 |) <----- 0 : {-3, |
|                                                                0            |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|a2b2c2-ab4d ab2c3-ab3d2 ab2c2-a2bcd ab4c-a3bc2 a2bc3-ab3cd abc4-ab2cd2 ab2cd-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|c3  0         0          abc2d a2c2d 0         abcd2 abcd2 ac4   abcd2 0     |
|    ac3       0          0     0     ac2d      0     0     0     0     acd2  |
|cd  a2c2+ab2d ac3-abd2   abd2  a2d2  abc2+a2cd ac2d  ac2d  ac2d  ac2d  abcd+a|
|2bc -ab3      -a2c2+ab2d -ab2d -a2bd -a2bc     -a2cd -a2cd -abc2 -a2cd -a2bd |
|                                                                             |
|0 0 0 0 0 0 0 0 -abc2d -ab2cd -a2bcd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|0 0 0 0 0 0 0 0 abc3   ab2c2  a2bc2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|0 0 0 0 0 0 0 0 ab2c2  ab3c   a2b2c  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|0 0 0 0 0 0 0 0 -a2bc2 -a2b2c -a3bc  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|-----------------------------------------------------------------------------|
|a2bcd3 a2bcd2-a3d3 a2b3d2-a4cd2 a3c2d2-a2b2d3 a2c3d2-a2bd4 ab4c-a2b3d ab6-a3b|
|                                                                             |
|                                                                             |
|ab3d2 -a2bcd2 -ab2d3 -abc2d2 -ab2c3 -a2c4 -abc3d -ac5  -ab2c2d -a2c3d -abc2d2|
|bcd2  abd3    0      0       ac4    ac3d  0      0     ac3d    ac2d2  0      |
|2bd2  ab2d2   -abcd2 -abd3   a2c3   abc3  -ac4   -ac3d a2c2d   abc2d  -ac3d  |
|      0       a2bd2  ab2d2   0      0     a2c3   abc3  0       0      a2c2d  |
|                                                                             |
|2  bcd3   bd4   c4d  c3d2  c2d3   cd4   d5   0 0 0 0 |) <----- 0 : {-5, 7}   |
|d  -bc2d2 -bcd3 -c5  -c4d  -c3d2  -c2d3 -cd4 0 0 0 0 |     0                 |
|2d -b2cd2 -b2d3 -bc4 -bc3d -bc2d2 -bcd3 -bd4 0 0 0 0 |                       |
|d  abcd2  abd3  ac4  ac3d  ac2d2  acd3  ad4  0 0 0 0 |                       |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | : {-1, 2}                            |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 |                                      |
|0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 |                                      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a |                                      |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0  0  0  |) <----- 0 : {-1, 3}                                              |
| d2 0  0  |     0                                                            |
| 0  d2 0  |                                                                  |
| 0  0  d2 |                                                                  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| b2d bc2 bcd bd2 c3 c2d cd2 d3 |) <------------------------------- cokernel {|
|                                     {2} | 1 0 0 0 0 0 0 0 0 0 |            {|
|                                     {2} | 0 1 0 0 0 0 0 0 0 0 |            {|
|                                     {2} | 0 0 1 0 0 0 0 0 0 0 |            {|
|                                     {2} | 0 0 0 1 0 0 0 0 0 0 |            {|
|                                     {2} | 0 0 0 0 1 0 0 0 0 0 |            {|
|                                     {2} | 0 0 0 0 0 1 0 0 0 0 |            {|
|                                     {2} | 0 0 0 0 0 0 1 0 0 0 |            {|
|                                     {2} | 0 0 0 0 0 0 0 1 0 0 |            {|
|                                     {2} | 0 0 0 0 0 0 0 0 1 0 |            {|
|                                     {2} | 0 0 0 0 0 0 0 0 0 1 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {4} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {4} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {4} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {4} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {4} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {4} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {4} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {4} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {4} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {4} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {4} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {4} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                                                             |
|  bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0   0   d3 0  0  0  |, |
|  0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0   0   0  d3 0  0  |  |
|  0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2 0   0  0  d3 0  |  |
|d 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0   cd2 0  0  0  d3 |  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|c3 bc2 ac2 0   0  0   0   0   0  0   0   0   0  0   0   0   0   0   0   0   0|
|0  0   0   c2d c3 bc2 ac2 0   0  0   0   0   0  0   0   cd2 c2d bcd acd 0   0|
|0  0   0   0   0  0   0   c2d c3 bc2 ac2 0   0  0   0   0   0   0   0   cd2 c|
|0  0   0   0   0  0   0   0   0  0   0   c2d c3 bc2 ac2 0   0   0   0   0   0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-bcd3 bcd2-ad3 b3d2-a2cd2 ac2d2-b2d3 c3d2-bd4 a4 a3b a3c a3d a2b2 a2bc a2bd a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|  0         0 0 0 0 0 0 0 0 0 0 0 0 0 0          0 0          0          0 0 |
|  -a2cd     0 0 0 0 0 0 0 0 0 0 0 0 0 -a2c2+ab2d 0 -abcd      -abcd      0 0 |
|d -a2bc-a3d 0 0 0 0 0 0 0 0 0 0 0 0 0 ab3-a3c    0 -ab2c-a2bd -ab2c-a2bd 0 0 |
|  a3b       0 0 0 0 0 0 0 0 0 0 0 0 0 0          0 a2b2       a2b2       0 0 |
|                                                                             |
| 0 0 0 0 0 a2d  abd  acd  ad2  b2d  bcd  bd2  c2d  cd2  d3   a4 0  0  0  a3b |
| 0 0 0 0 0 -a2c -abc -ac2 -acd -b2c -bc2 -bcd -c3  -c2d -cd2 0  a4 0  0  0   |
| 0 0 0 0 0 -a2b -ab2 -abc -abd -b3  -b2c -b2d -bc2 -bcd -bd2 0  0  a4 0  0   |
| 0 0 0 0 0 a3   a2b  a2c  a2d  ab2  abc  abd  ac2  acd  ad2  0  0  0  a4 0   |
|                                                                             |
|6}                                                                           |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|a2bd2 ab4d-a3bcd a2bc2d-ab3d2 abc3d-ab2d3 abc3-a2c2d ab3c2-a3c3 a2c4-ab2c2d a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|    abd3  ac3d  ac3d  abd3  0 a2cd2 a2cd2 a2cd2 ac2d2 ac2d2 ab4   ab3c  b5   |
|    0     0     0     0     0 -ad3  -ad3  -ad3  0     0     -ab2c -abc2 -b3c |
|2d2 acd2  acd2  acd2  acd2  0 -abd2 -abd2 -abd2 ad3   ad3   -a2b2 -a2bc -ab3 |
|    -a2d2 -abcd -abcd -a2d2 0 0     0     0     -abd2 -abd2 0     0     0    |
|                                                                             |
|0 0 0 0 -ac3d -abc2d -a2c2d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 ac4   abc3   a2c3   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 abc3  ab2c2  a2bc2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 -a2c3 -a2bc2 -a3c2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|-----------------------------------------------------------------------------|
|3c a2b3c2-ab5d ab3c3-ab4d2 ab3c2-a2b2cd ab5c-a3b2c2 a2b2c3-ab4cd ab2c4-ab3cd2|
|                                                                             |
|                                                                             |
| -ac4d  -ab2cd2 -a2c2d2 -abcd3 -ac3d2 -ab2d3 -a2cd3 -abd4 -ac2d3 -b6 -ab4c -b|
| 0      ac2d2   acd3    0      0      acd3   ad4    0     0      b4c b4d   0 |
| -ac2d2 a2cd2   abcd2   -ac2d2 -acd3  a2d3   abd3   -acd3 -ad4   ab4 b5    -b|
| abc2d  0       0       a2cd2  abcd2  0      0      a2d3  abd3   0   0     ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|2} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|2} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|2} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 |
|2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 |
|2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 |
|2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a |
|2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|{2} | -ab2 -a2c -abd -ac2 -b3 -abc -b2d -bc2 -b2c -ac2 -bcd -c3 -b2d -acd -bd|
|{3} | ac   ad   0    0    bc  bd   0    0    c2   cd   0    0   cd   d2   0  |
|{3} | a2   ab   -ac  -ad  ab  b2   -bc  -bd  ac   bc   -c2  -cd ad   bd   -cd|
|{3} | 0    0    a2   ab   0   0    ab   b2   0    0    ac   bc  0    0    ad |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|   0   0   0   0   0   0   0  0   0   0   0  0   0   0   0  0   0   0   ad  b|
|   0   0   0   0   0   0   d3 cd2 bd2 ad2 0  0   0   0   0  0   0   0   -ac -|
|2d bcd acd 0   0   0   0   0  0   0   0   d3 cd2 bd2 ad2 0  0   0   0   -ab -|
|   0   0   cd2 c2d bcd acd 0  0   0   0   0  0   0   0   d3 cd2 bd2 ad2 a2  a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2c2 a2cd a2d2 ab3 ab2c ab2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0 0 0 0 0         0 0 0 0 0 0 0 0 0 0         0          0         0         |
|0 0 0 0 -ac3+abd2 0 0 0 0 0 0 0 0 0 -abc2+b3d -a2c2+ab2d -ac3+abd2 -ac3+b2cd+|
|0 0 0 0 0         0 0 0 0 0 0 0 0 0 b4-a2bc   ab3-a3c    0         b3c+ab2d  |
|0 0 0 0 ab3-a3c   0 0 0 0 0 0 0 0 0 0         0          ab3-a3c   -a3c      |
|                                                                             |
|0   0   0   a3c 0   0   0   a3d 0   0   0   a2b2 0    0    0    a2bc 0    0  |
|a3b 0   0   0   a3c 0   0   0   a3d 0   0   0    a2b2 0    0    0    a2bc 0  |
|0   a3b 0   0   0   a3c 0   0   0   a3d 0   0    0    a2b2 0    0    0    a2b|
|0   0   a3b 0   0   0   a3c 0   0   0   a3d 0    0    0    a2b2 0    0    0  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|c5-abc2d2 abc2d-a2cd2 ab3cd-a3c2d a2c3d-ab2cd2 ac4d-abcd3 abcd2-a2d3 ab3d2-a3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|b4d  b4d  ab3d  0         b3c2 b3c2 ab2c2 b4c   b4c   b3cd  b3cd  b3cd  ab2cd|
|0    0    0     -abc2+b3d 0    0    0     -b2c2 -b2c2 0     0     0     0    |
|b3c  b3c  ab2c  b4-a2bc   b3d  b3d  ab2d  -ab2c -ab2c b2c2  b2c2  b2c2  abc2 |
|-ab3 -ab3 -a2b2 0         -b4  -b4  -ab3  0     0     -ab2c -ab2c -ab2c -a2bc|
|                                                                             |
| 0 0 0 0 0 0 0 0 -b4d -ab3d 0 0 0 -b3cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -b2|
| 0 0 0 0 0 0 0 0 b4c  ab3c  0 0 0 b3c2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b2c|
| 0 0 0 0 0 0 0 0 b5   ab4   0 0 0 b4c   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b3c|
| 0 0 0 0 0 0 0 0 -ab4 -a2b3 0 0 0 -ab3c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -ab|
|-----------------------------------------------------------------------------|
| ab3cd-a2b2d2 ab5d-a3b2cd a2b2c2d-ab4d2 ab2c3d-ab3d3 ab2c3-a2bc2d ab4c2-a3bc3|
|                                                                             |
|                                                                             |
|5d -b4c2 -b5c -ab3c2 -b4cd -b3c3 -b5d -ab3cd -b4d2 -b3c2d -b4c2 -ab2c3 -b3c2d|
|   0     b3c2 b3cd   0     0     b3cd b3d2   0     0      b2c3  b2c2d  0     |
|4c -b4d  ab3c b4c    -b3c2 -b3cd ab3d b4d    -b3cd -b3d2  ab2c2 b3c2   -b2c3 |
|4  b5    0    0      ab3c  b4c   0    0      ab3d  b4d    0     0      ab2c2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0 0 0 0 | : {-2, 2}                                                          |
|0 0 0 0 |                                                                    |
|0 0 0 0 |                                                                    |
|0 0 0 0 |                                                                    |
|0 0 0 0 |                                                                    |
|0 0 0 0 |                                                                    |
|0 0 0 0 |                                                                    |
|0 0 0 0 |                                                                    |
|0 0 0 0 |                                                                    |
|d c b a |                                                                    |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2 -c2d a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0 |
|  0    0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0 |
|  -d2  0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab|
|  bd   0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|d  cd  d2  a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0 |
|bc -c2 -cd 0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab|
|b2 -bc -bd 0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0 |
|b  ac  ad  0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|b2cd b2d2 bc3 bc2d bcd2 bd3 c4 c3d c2d2 cd3 d4 |, | a2bc-a3d a2b3-a4c a3c2-a2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|     0 0 0 0 0 0         0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a2b2 -a3c -a2bd -a2c2 -|
|abd2 0 0 0 0 0 -bc3+ac2d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a2c   a2d  0     0     a|
|     0 0 0 0 0 -b3d+a2cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a3    a2b  -a2c  -a2d  a|
|     0 0 0 0 0 b4-a2bc   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0     0    a3    a2b   0|
|                                                                             |
|  0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    |
|  0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 |
|c 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    |
|  a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|cd2 a2c2d2-ab2d3 ac3d2-abd4 b4c-ab3d b6-a2b3c ab3c2-b5d b3c3-b4d2 b3c2-ab2cd |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0        b3d2  b2c3 b3d2  ab2d2 0        b2c2d b2c2d b2c3 abc3  0        0  |
| b2cd     0     0    0     0     b2d2     0     0     0    0     bc3      0  |
| b3c+ab2d b2cd  b2cd b2cd  abcd  abc2+b3d b2d2  b2d2  b2cd abcd  abc2+b3d bc3|
| -ab3     -ab2d -b3c -ab2d -a2bd -a2bc    -b3d  -b3d  -b3c -ab2c -b4      -ab|
|                                                                             |
|c2d -b3cd -ab2cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -bc3d -b2c2d|
|3   b3c2  ab2c2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 bc4   b2c3  |
|2   b4c   ab3c   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b2c3  b3c2  |
|2c2 -ab3c -a2b2c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -abc3 -ab2c2|
|-----------------------------------------------------------------------------|
| a2bc4-ab3c2d abc5-ab2c2d2 ab2c2d-a2bcd2 ab4cd-a3bc2d a2bc3d-ab3cd2 abc4d-ab2|
|                                                                             |
|                                                                             |
| -b2c4  -b4cd -ab2c2d -b3cd2 -b2c3d -b4d2 -ab2cd2 -b3d3  -b2c2d2 -b3c3 -abc4 |
| 0      b2c2d b2cd2   0      0      b2cd2 b2d3    0      0       bc4   bc3d  |
| -b2c2d ab2cd b3cd    -b2c2d -b2cd2 ab2d2 b3d2    -b2cd2 -b2d3   abc3  b2c3  |
| b3c2   0     0       ab2cd  b3cd   0     0       ab2d2  b3d2    0     0     |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|  0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0  |
|  0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2|
|2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0  |
|  ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|  0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2|
|2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0  |
|  ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0  |
|  0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|b2d a2c3-a2bd2 ab2c-a2bd ab4-a3bc a2bc2-ab3d abc3-ab2d2 abc2-a2cd ab3c-a3c2 a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|ab3 -a2bc -ab2d -abc2 -ab2c -a2c2 -abcd -ac3 -ab2d -a2cd -abd2 -ac2d -b4 -ab2|
|bc  abd   0     0     ac2   acd   0     0    acd   ad2   0     0     b2c b2d |
|2b  ab2   -abc  -abd  a2c   abc   -ac2  -acd a2d   abd   -acd  -ad2  ab2 b3  |
|    0     a2b   ab2   0     0     a2c   abc  0     0     a2d   abd   0   0   |
|                                                                             |
|0    0    ab3 0   0   0   ab2c 0    0    0    ab2d 0    0    0    abc2 0    0|
|0    0    0   ab3 0   0   0    ab2c 0    0    0    ab2d 0    0    0    abc2 0|
|a2d2 0    0   0   ab3 0   0    0    ab2c 0    0    0    ab2d 0    0    0    a|
|0    a2d2 0   0   0   ab3 0    0    0    ab2c 0    0    0    ab2d 0    0    0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|b5c-a2b2c2 ab2c3-b4cd b2c4-b3cd2 b3cd-ab2d2 b5d-a2b2cd ab2c2d-b4d2 b2c3d-b3d3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|       b2c2d abc2d 0         b2cd2 b2cd2 bc4   b2cd2 abcd2 0         b2d3  bc|
|       0     0     bc2d      0     0     0     0     0     bcd2      0     0 |
|-b2d2  b2d2  abd2  b2c2+abcd bc2d  bc2d  bc2d  bc2d  ac2d  b2cd+abd2 bcd2  bc|
|c2+b3d -b3d  -ab2d -ab2c     -abcd -abcd -b2c2 -abcd -a2cd -ab2d     -abd2 -b|
|                                                                             |
| -abc2d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -c4|
| abc3   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c5 |
| ab2c2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 bc4|
| -a2bc2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -ac|
|-----------------------------------------------------------------------------|
|cd3 ab2cd2-a2bd3 ab4d2-a3bcd2 a2bc2d2-ab3d3 abc3d2-ab2d4 abc4-a2c3d ab3c3-a3c|
|                                                                             |
|                                                                             |
|-b2c3d -bc5  -b3c2d -abc3d -b2c2d2 -bc4d  -b3cd2 -abc2d2 -b2cd3 -bc3d2 -b3d3 |
|0      0     bc3d   bc2d2  0       0      bc2d2  bcd3    0      0      bcd3  |
|-bc4   -bc3d abc2d  b2c2d  -bc3d   -bc2d2 abcd2  b2cd2   -bc2d2 -bcd3  abd3  |
|abc3   b2c3  0      0      abc2d   b2c2d  0      0       abcd2  b2cd2  0     |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   |
| 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd |
| ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   |
| 0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd |
| ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   |
| 0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   |
| 0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2c3-ab2cd ac4-abcd2 abcd-a2d2 ab3d-a3cd a2c2d-ab2d2 ac3d-abd3 b3c-ab2d b5-a2b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|c -b3d -b2c2 -b3c -abc2 -b2cd -bc3 -b3d -abcd -b2d2 -bc2d -b2c2 -ac3 -bc2d -c|
|  0    0     bc2  bcd   0     0    bcd  bd2   0     0     c3    c2d  0     0 |
|  -b2c -b2d  abc  b2c   -bc2  -bcd abd  b2d   -bcd  -bd2  ac2   bc2  -c3   -c|
|  ab2  b3    0    0     abc   b2c  0    0     abd   b2d   0     0    ac2   bc|
|                                                                             |
|    0    abcd 0    0    0    abd2 0    0    0    ac3 0   0   0   ac2d 0    0 |
|    0    0    abcd 0    0    0    abd2 0    0    0   ac3 0   0   0    ac2d 0 |
|bc2 0    0    0    abcd 0    0    0    abd2 0    0   0   ac3 0   0    0    ac|
|    abc2 0    0    0    abcd 0    0    0    abd2 0   0   0   ac3 0    0    0 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| b2c3-abc2d b4c2-a2bc3 abc4-b3c2d bc5-b2c2d2 b2c2d-abcd2 b4cd-a2bc2d abc3d-b3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|3d  bc3d  b2d3  abd3  0         bc2d2 bc2d2 c5             bc4   ac4   0     |
|    0     0     0     bd3       0     0     0              0     0     c4    |
|d2  bcd2  bcd2  acd2  ac2d+b2d2 bd3   bd3   bd3            bc2d  ac2d  b2cd+a|
|2cd -b2cd -abd2 -a2d2 -a2cd     -b2d2 -b2d2 -bc3+ac2d-b2d2 -b2c2 -abc2 -b3c+a|
|                                                                             |
|d -bc3d -ac3d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|  bc4   ac4   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|  b2c3  abc3  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|4 -abc3 -a2c3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|-----------------------------------------------------------------------------|
|4 a2c5-ab2c3d ac6-abc3d2 abc3d-a2c2d2 ab3c2d-a3c3d a2c4d-ab2c2d2 ac5d-abc2d3 |
|                                                                             |
|                                                                             |
|-abcd3 -b2d4 -bc2d3 -b2c4 -ac5 -bc4d -c6  -b2c3d -ac4d -bc3d2 -c5d  -b2c2d2 -|
|bd4    0     0      c5    c4d  0     0    c4d    c3d2  0      0     c3d2    c|
|b2d3   -bcd3 -bd4   ac4   bc4  -c5   -c4d ac3d   bc3d  -c4d   -c3d2 ac2d2   b|
|0      abd3  b2d3   0     0    ac4   bc4  0      0     ac3d   bc3d  0       0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0   0   d3 0  0  |
|0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0   0   0  d3 0  |
|bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2 0   0  0  d3 |
|0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0   cd2 0  0  0  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0   0   d3 0 |
|bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0   0   0  d3|
|0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2 0   0  0 |
|0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0   cd2 0  0 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2c ab2c2-b4d b2c3-b3d2 b2c2-abcd b4c-a2bc2 abc3-b3cd bc4-b2cd2 b2cd-abd2 b4d-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|4  -b2cd -ac2d -bcd2 -c3d -b2d2 -acd2 -bd3 -c2d2 a4 0  0  0  a3b 0   0   0   |
|   c2d   cd2   0     0    cd2   d3    0    0     0  a4 0  0  0   a3b 0   0   |
|2d acd   bcd   -c2d  -cd2 ad2   bd2   -cd2 -d3   0  0  a4 0  0   0   a3b 0   |
|2  0     0     acd   bcd  0     0     ad2  bd2   0  0  0  a4 0   0   0   a3b |
|                                                                             |
|   0    acd2 0    0    0    ad3 0   0   0   b4 0  0  0  b3c 0   0   0   b3d 0|
|   0    0    acd2 0    0    0   ad3 0   0   0  b4 0  0  0   b3c 0   0   0   b|
|2d 0    0    0    acd2 0    0   0   ad3 0   0  0  b4 0  0   0   b3c 0   0   0|
|   ac2d 0    0    0    acd2 0   0   0   ad3 0  0  0  b4 0   0   0   b3c 0   0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|cd2 bc4d-b2cd3 b2cd2-abd3 b4d2-a2bcd2 abc2d2-b3d3 bc3d2-b2d4 bc4-ac3d b3c3-a2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|         0         bc3d  ac3d  0         0          bc2d2 ac2d2 0         bcd|
|         0         0     0     c3d       0          0     0     c2d2      0  |
|bd2      c4-bcd2   bcd2  acd2  ac2d+b2d2 c3d-bd3    bd3   ad3   bc2d+acd2 c2d|
|2c2-ab2d -ac3+b2cd -b2cd -abcd -b3d      -ac2d+b2d2 -b2d2 -abd2 -abcd     -ac|
|                                                                             |
| 0 0 0 0 0 0 0 0 a3d  a2bd  a2cd  a2d2  ab2d  abcd  abd2  ac2d  acd2  ad3   b|
| 0 0 0 0 0 0 0 0 -a3c -a2bc -a2c2 -a2cd -ab2c -abc2 -abcd -ac3  -ac2d -acd2 -|
| 0 0 0 0 0 0 0 0 -a3b -a2b2 -a2bc -a2bd -ab3  -ab2c -ab2d -abc2 -abcd -abd2 -|
| 0 0 0 0 0 0 0 0 a4   a3b   a3c   a3d   a2b2  a2bc  a2bd  a2c2  a2cd  a2d2  a|
|-----------------------------------------------------------------------------|
|abc2d2-a2cd3 ab3cd2-a3c2d2 a2c3d2-ab2cd3 ac4d2-abcd4 abcd3-a2d4 ab3d3-a3cd3 a|
|                                                                             |
|                                                                             |
|ac3d2 -bc2d3 -c4d2 -b2cd3 -ac2d3 -bcd4 -c3d3 -b2d4 -acd4 -bd5 -c2d4 0 0 0 0 ||
|2d3   0      0     c2d3   cd4    0     0     cd4   d5    0    0     0 0 0 0 ||
|c2d2  -c3d2  -c2d3 acd3   bcd3   -c2d3 -cd4  ad4   bd4   -cd4 -d5   0 0 0 0 ||
|      ac2d2  bc2d2 0      0      acd3  bcd3  0     0     ad4  bd4   0 0 0 0 ||
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0  |) <------------------------------------------------------------------- co|
|0  |     {4} | 1 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|0  |     {5} | 0 1 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|d3 |     {5} | 0 0 0 0 0 -1 0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 -1 0 0 0 0  0 0 0 0  0 0 |     |
|         {4} | 0 0 1 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 1 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 -1 0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 -1 0 0 0 0  0 0 |     |
|         {4} | 0 0 0 0 1 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  1 0 0 0  0 0 0 0  0 0 |     |
|         {4} | 0 0 0 0 0 0  1 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  1 0 0 0  0 0 |     |
|         {4} | 0 0 0 0 0 0  0 1 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 1 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 -1 0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 -1 0 0 |     |
|         {4} | 0 0 0 0 0 0  0 0 0 1 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {4} | 0 0 0 0 0 0  0 0 0 0 0  1 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  1 0 |     |
|         {4} | 0 0 0 0 0 0  0 0 0 0 0  0 0  1 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 1 0 0  0 0 0 0  0 0 |     |
|         {4} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 1 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 1 0 0  0 0 |     |
|         {4} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 1 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 1 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|                                                                             |
| 0  0  |, {4} | ad  bd  cd  d2  a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a|
| 0  0  |  {4} | -ac -bc -c2 -cd 0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0|
| d3 0  |  {4} | -ab -b2 -bc -bd 0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0|
| 0  d3 |  {4} | a2  ab  ac  ad  0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|a2bcd abc2d-b3d2 bc3d-b2d3 bc3-ac2d b3c2-a2c3 ac4-b2c2d c5-bc2d2 bc2d-acd2 b3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|a3c 0   0   0   a3d 0   0   0   a2b2 0    0    0    a2bc 0    0    0    a2bd |
|0   a3c 0   0   0   a3d 0   0   0    a2b2 0    0    0    a2bc 0    0    0    |
|0   0   a3c 0   0   0   a3d 0   0    0    a2b2 0    0    0    a2bc 0    0    |
|0   0   0   a3c 0   0   0   a3d 0    0    0    a2b2 0    0    0    a2bc 0    |
|                                                                             |
|   0   0   b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0    bc3 0 |
|3d 0   0   0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0   bc|
|   b3d 0   0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0   0 |
|   0   b3d 0    0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0   0 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|c4 ac5-b2c3d c6-bc3d2 bc3d-ac2d2 b3c2d-a2c3d ac4d-b2c2d2 c5d-bc2d3 bc2d2-acd3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|3  bcd3  c4d   c4d   bcd3  0        bd4  c3d2  c3d2  0 bd4  0 acd3 acd3 acd3 |
|   0     0     0     0     cd3      0    0     0     0 0    0 -d4  -d4  -d4  |
|2  c2d2  c2d2  c2d2  c2d2  bcd2+ad3 cd3  cd3   cd3   0 cd3  0 -bd3 -bd3 -bd3 |
|d2 -acd2 -bc2d -bc2d -acd2 -abd2    -ad3 -bcd2 -bcd2 0 -ad3 0 0    0    0    |
|                                                                             |
|3d  b2cd  b2d2  bc2d  bcd2  bd3   c3d  c2d2  cd3   d4   0 0 0 0 |, {4} | a3d |
|b3c -b2c2 -b2cd -bc3  -bc2d -bcd2 -c4  -c3d  -c2d2 -cd3 0 0 0 0 |  {4} | -a3c|
|b4  -b3c  -b3d  -b2c2 -b2cd -b2d2 -bc3 -bc2d -bcd2 -bd3 0 0 0 0 |  {4} | -a3b|
|b3  ab2c  ab2d  abc2  abcd  abd2  ac3  ac2d  acd2  ad3  0 0 0 0 |  {4} | a4  |
|-----------------------------------------------------------------------------|
|2c2d3-ab2d4 ac3d3-abd5 b5c-ab4d b7-a2b4c ab4c2-b6d b4c3-b5d2 b4c2-ab3cd b6c-a|
|                                                                             |
|                                                                             |
|, {2} | -a4b2 -a5c -a4bd -a4c2 -a3b3 -a4bc -a3b2d -a3bc2 -a3b2c -a4c2 -a3bcd |
|  {3} | a4c   a4d  0     0     a3bc  a3bd  0      0      a3c2   a3cd  0      |
|  {3} | a5    a4b  -a4c  -a4d  a4b   a3b2  -a3bc  -a3bd  a4c    a3bc  -a3c2  |
|  {3} | 0     0    a5    a4b   0     0     a4b    a3b2   0      0     a4c    |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|kernel {4} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {4} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {4} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {4} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0 |
|   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0 |
|   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0 |
|   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|cd-a2c2d ac3d-b2cd2 c4d-bcd3 bcd2-ad3 b3d2-a2cd2 ac2d2-b2d3 c3d2-bd4 a4 a3b a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0    0    ab|
|a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0    0 |
|0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0 |
|0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0 |
|                                                                             |
|  0   0   bc2d 0    0    0    bcd2 0    0    0    bd3 0   0   0   c4 0  0  0 |
|3 0   0   0    bc2d 0    0    0    bcd2 0    0    0   bd3 0   0   0  c4 0  0 |
|  bc3 0   0    0    bc2d 0    0    0    bcd2 0    0   0   bd3 0   0  0  c4 0 |
|  0   bc3 0    0    0    bc2d 0    0    0    bcd2 0   0   0   bd3 0  0  0  c4|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| b3cd2-a2c2d2 ac3d2-b2cd3 c4d2-bcd4 bcd3-ad4 b3d3-a2cd3 ac2d3-b2d4 c3d3-bd5 0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|c2d3 c2d3 0 0 0         0         0 0 0 0 0 0 0 0 0 0 0 0 0 0           0 0  |
|0    0    0 0 -a3cd     -a3cd     0 0 0 0 0 0 0 0 0 0 0 0 0 -a3c2+a2b2d 0 -a2|
|d4   d4   0 0 -a3bc-a4d -a3bc-a4d 0 0 0 0 0 0 0 0 0 0 0 0 0 a2b3-a4c    0 -a2|
|-bd3 -bd3 0 0 a4b       a4b       0 0 0 0 0 0 0 0 0 0 0 0 0 0           0 a3b|
|                                                                             |
| a2bd  a2cd  a2d2  ab2d  abcd  abd2  ac2d  acd2  ad3   b3d  b2cd  b2d2  bc2d |
| -a2bc -a2c2 -a2cd -ab2c -abc2 -abcd -ac3  -ac2d -acd2 -b3c -b2c2 -b2cd -bc3 |
| -a2b2 -a2bc -a2bd -ab3  -ab2c -ab2d -abc2 -abcd -abd2 -b4  -b3c  -b3d  -b2c2|
| a3b   a3c   a3d   a2b2  a2bc  a2bd  a2c2  a2cd  a2d2  ab3  ab2c  ab2d  abc2 |
|-----------------------------------------------------------------------------|
|2b3c2 ab3c3-b5cd b3c4-b4cd2 b4cd-ab3d2 b6d-a2b3cd ab3c2d-b5d2 b3c3d-b4d3 b3c3|
|                                                                             |
|                                                                             |
|-a3c3 -a3b2d -a4cd -a3bd2 -a3c2d -a2b4 -a3b2c -a2b3d -a2b2c2 -a2b3c -a3bc2 -a|
|0     a3cd   a3d2  0      0      a2b2c a2b2d  0      0       a2bc2  a2bcd  0 |
|-a3cd a4d    a3bd  -a3cd  -a3d2  a3b2  a2b3   -a2b2c -a2b2d  a3bc   a2b2c  -a|
|a3bc  0      0     a4d    a3bd   0     0      a3b2   a2b3    0      0      a3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|  acd 0   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0  |
|  0   acd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0  |
|  0   0   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0  |
|2 0   0   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab2d abc2 abcd abd2 ac3 ac2d ac|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|3 0   0   0   ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abc|
|  ab3 0   0   0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0  |
|  0   ab3 0   0    0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0  |
|  0   0   ab3 0    0    0    ab2c 0    0    0    ab2d 0    0    0    abc2 0  |
|                                                                             |
| c3d 0   0   0   c2d2 0    0    0    cd3 0   0   0   d4 0  0  0  |, {4} | a2d|
| 0   c3d 0   0   0    c2d2 0    0    0   cd3 0   0   0  d4 0  0  |  {4} | -a2|
| 0   0   c3d 0   0    0    c2d2 0    0   0   cd3 0   0  0  d4 0  |  {4} | -a2|
| 0   0   0   c3d 0    0    0    c2d2 0   0   0   cd3 0  0  0  d4 |  {4} | a3 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| |, | a3bc-a4d a3b3-a5c a4c2-a3b2d a3c3-a3bd2 a2b2c-a3bd a2b4-a4bc a3bc2-a2b3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|         0           0 0 0 0 0 0 0           0 0 0 0 0 0 0 0 0 0           0 |
|bcd      -a2bcd      0 0 0 0 0 0 -a2c3+a2bd2 0 0 0 0 0 0 0 0 0 -a2bc2+ab3d -a|
|b2c-a3bd -a2b2c-a3bd 0 0 0 0 0 0 0           0 0 0 0 0 0 0 0 0 ab4-a3bc    a2|
|2        a3b2        0 0 0 0 0 0 a2b3-a4c    0 0 0 0 0 0 0 0 0 0           0 |
|                                                                             |
| bcd2  bd3   c3d  c2d2  cd3   d4   0 0 0 0 |) <----- 0 : {-4, 6}             |
| -bc2d -bcd2 -c4  -c3d  -c2d2 -cd3 0 0 0 0 |     0                           |
| -b2cd -b2d2 -bc3 -bc2d -bcd2 -bd3 0 0 0 0 |                                 |
| abcd  abd2  ac3  ac2d  acd2  ad3  0 0 0 0 |                                 |
|-----------------------------------------------------------------------------|
|-ab2c2d b5c2-a2b2c3 ab2c4-b4c2d b2c5-b3c2d2 b3c2d-ab2cd2 b5cd-a2b2c2d ab2c3d-|
|                                                                             |
|                                                                             |
|2b2cd -a2bc3 -a2b3d -a3bcd -a2b2d2 -a2bc2d -a2b2c2 -a3c3 -a2bc2d -a2c4  -a2b2|
|      0      a2bcd  a2bd2  0       0       a2c3    a2c2d 0       0      a2c2d|
|2bc2  -a2bcd a3bd   a2b2d  -a2bcd  -a2bd2  a3c2    a2bc2 -a2c3   -a2c2d a3cd |
|bc    a2b2c  0      0      a3bd    a2b2d   0       0     a3c2    a2bc2  0    |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | : {-2, 3}       |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a |                 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| bc2 0   0   0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   |
| 0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   |
| 0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   |
| 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|d2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 bd3 c4 c3d c2d2 cd3 d4 |) <---|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                             |
|d 0    0    0    abd2 0    0    0    ac3 0   0   0   ac2d 0    0    0    acd2|
|  abcd 0    0    0    abd2 0    0    0   ac3 0   0   0    ac2d 0    0    0   |
|  0    abcd 0    0    0    abd2 0    0   0   ac3 0   0    0    ac2d 0    0   |
|  0    0    abcd 0    0    0    abd2 0   0   0   ac3 0    0    0    ac2d 0   |
|                                                                             |
|  abd  acd  ad2  b2d  bcd  bd2  c2d  cd2  d3   a4 0  0  0  a3b 0   0   0   a3|
|c -abc -ac2 -acd -b2c -bc2 -bcd -c3  -c2d -cd2 0  a4 0  0  0   a3b 0   0   0 |
|b -ab2 -abc -abd -b3  -b2c -b2d -bc2 -bcd -bd2 0  0  a4 0  0   0   a3b 0   0 |
|  a2b  a2c  a2d  ab2  abc  abd  ac2  acd  ad2  0  0  0  a4 0   0   0   a3b 0 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|d a2bc3-a2b2d2 a2bc2-a3cd a2b3c-a4c2 a3c3-a2b2cd a2c4-a2bcd2 a2bcd-a3d2 a2b3d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|          0           0                 0 0 0 0 0 0           0 0 0 0 0 0 0 0|
|3c2+a2b2d -a2c3+a2bd2 -a2c3+ab2cd+a2bd2 0 0 0 0 0 -abc3+a2c2d 0 0 0 0 0 0 0 0|
|b3-a4c    0           ab3c+a2b2d        0 0 0 0 0 -ab3d+a3cd  0 0 0 0 0 0 0 0|
|          a2b3-a4c    -a4c              0 0 0 0 0 ab4-a3bc    0 0 0 0 0 0 0 0|
|-----------------------------------------------------------------------------|
|b4cd2 b2c4d-b3cd3 b3cd2-ab2d3 b5d2-a2b2cd2 ab2c2d2-b4d3 b2c3d2-b3d4 b2c4-abc3|
|                                                                             |
|                                                                             |
|cd -a3c2d -a2bcd2 -a2c3d -a2b2d2 -a3cd2 -a2bd3 -a2c2d2 -ab5 -a2b3c -ab4d -ab3|
|   a2cd2  0       0      a2cd2   a2d3   0      0       ab3c ab3d   0     0   |
|   a2bcd  -a2c2d  -a2cd2 a3d2    a2bd2  -a2cd2 -a2d3   a2b3 ab4    -ab3c -ab3|
|   0      a3cd    a2bcd  0       0      a3d2   a2bd2   0    0      a2b3  ab4 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|cd2 0   0   0   d3 0  0  0  |) <----- 0 : {-2, 4}                            |
|0   cd2 0   0   0  d3 0  0  |     0                                          |
|0   0   cd2 0   0  0  d3 0  |                                                |
|0   0   0   cd2 0  0  0  d3 |                                                |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|------------------------------------------------ cokernel {3} | d c b a 0 0 0|
|3} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 d c b|
|3} | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|                                                                             |
| 0    0    0    ad3 0   0   0   b4 0  0  0  b3c 0   0   0   b3d 0   0   0   b|
| acd2 0    0    0   ad3 0   0   0  b4 0  0  0   b3c 0   0   0   b3d 0   0   0|
| 0    acd2 0    0   0   ad3 0   0  0  b4 0  0   0   b3c 0   0   0   b3d 0   0|
| 0    0    acd2 0   0   0   ad3 0  0  0  b4 0   0   0   b3c 0   0   0   b3d 0|
|                                                                             |
|c 0   0   0   a3d 0   0   0   a2b2 0    0    0    a2bc 0    0    0    a2bd 0 |
|  a3c 0   0   0   a3d 0   0   0    a2b2 0    0    0    a2bc 0    0    0    a2|
|  0   a3c 0   0   0   a3d 0   0    0    a2b2 0    0    0    a2bc 0    0    0 |
|  0   0   a3c 0   0   0   a3d 0    0    0    a2b2 0    0    0    a2bc 0    0 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-a4cd a3c2d-a2b2d2 a2c3d-a2bd3 ab3c-a2b2d ab5-a3b2c a2b2c2-ab4d ab2c3-ab3d2 a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0 0 0 0 0 0 0 0          0           0           0                0 0 0 0 0 |
| 0 0 0 0 0 0 0 -ab2c2+b4d -a2bc2+ab3d -abc3+a2c2d -abc3+b3cd+a2c2d 0 0 0 0 0 |
| 0 0 0 0 0 0 0 b5-a2b2c   ab4-a3bc    -ab3d+a3cd  b4c+a3cd         0 0 0 0 0 |
| 0 0 0 0 0 0 0 0          0           ab4-a3bc    -a3bc            0 0 0 0 0 |
|-----------------------------------------------------------------------------|
|d b4c3-a2bc4 abc5-b3c3d bc6-b2c3d2 b2c3d-abc2d2 b4c2d-a2bc3d abc4d-b3c2d2 bc5|
|                                                                             |
|                                                                             |
|c2 -ab4c -a2b2c2 -ab3cd -ab2c3 -ab4d -a2b2cd -ab3d2 -ab2c2d -ab3c2 -a2bc3 -ab|
|   ab2c2 ab2cd   0      0      ab2cd ab2d2   0      0       abc3   abc2d  0  |
|d  a2b2c ab3c    -ab2c2 -ab2cd a2b2d ab3d    -ab2cd -ab2d2  a2bc2  ab2c2  -ab|
|   0     0       a2b2c  ab3c   0     0       a2b2d  ab3d    0      0      a2b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0    bc3 0   0   0   bc|
|    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0   bc3 0   0   0 |
|    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0   0   bc3 0   0 |
|    0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0   0   0   bc3 0 |
|                                                                             |
|   0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0    0    ab3 |
|bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0    0   |
|   a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0   |
|   0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0   |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|b2c2-a2bcd ab4c-a3bc2 a2bc3-ab3cd abc4-ab2cd2 ab2cd-a2bd2 ab4d-a3bcd a2bc2d-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0           0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a3b2 -a4c -a3bd -a3c2 -a|
|-b2c3+abc2d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a3c   a3d  0     0     a2|
|-b4d+a2bcd  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a4    a3b  -a3c  -a3d  a3|
|b5-a2b2c    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0     0    a4    a3b   0 |
|-----------------------------------------------------------------------------|
|d-b2c2d3 b2c2d2-abcd3 b4cd2-a2bc2d2 abc3d2-b3cd3 bc4d2-b2cd4 b2cd3-abd4 b4d3-|
|                                                                             |
|                                                                             |
|2c2d -abc4  -ab3cd -a2bc2d -ab2cd2 -abc3d -ab3d2 -a2bcd2 -ab2d3 -abc2d2 -ab2c|
|     0      abc2d  abcd2   0       0      abcd2  abd3    0      0       ac4  |
|c3   -abc2d a2bcd  ab2cd   -abc2d  -abcd2 a2bd2  ab2d2   -abcd2 -abd3   a2c3 |
|c2   ab2c2  0      0       a2bcd   ab2cd  0      0       a2bd2  ab2d2   0    |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | : {-3|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a |      |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2d 0    0    0    bcd2 0    0    0    bd3 0   0   0   c4 0  0  0  c3d 0   0  |
|   bc2d 0    0    0    bcd2 0    0    0   bd3 0   0   0  c4 0  0  0   c3d 0  |
|   0    bc2d 0    0    0    bcd2 0    0   0   bd3 0   0  0  c4 0  0   0   c3d|
|   0    0    bc2d 0    0    0    bcd2 0   0   0   bd3 0  0  0  c4 0   0   0  |
|                                                                             |
|0   0   0   ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd |
|ab3 0   0   0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    |
|0   ab3 0   0    0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    |
|0   0   ab3 0    0    0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|b3d2 abc3d-ab2d3 abc3-a2c2d ab3c2-a3c3 a2c4-ab2c2d ac5-abc2d2 abc2d-a2cd2 ab3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2b3 -a3bc -a2b2d -a2bc2 -a2b2c -a3c2 -a2bcd -a2c3 -a2b2d -a3cd -a2bd2 -a2c2d |
|bc  a2bd  0      0      a2c2   a2cd  0      0     a2cd   a2d2  0      0      |
|b   a2b2  -a2bc  -a2bd  a3c    a2bc  -a2c2  -a2cd a3d    a2bd  -a2cd  -a2d2  |
|    0     a3b    a2b2   0      0     a3c    a2bc  0      0     a3d    a2bd   |
|-----------------------------------------------------------------------------|
|a2bcd3 abc2d3-b3d4 bc3d3-b2d5 bc5-ac4d b3c4-a2c5 ac6-b2c4d c7-bc4d2 bc4d-ac3d|
|                                                                             |
|                                                                             |
|3 -a2c4 -abc3d -ac5  -ab2c2d -a2c3d -abc2d2 -ac4d  -ab2cd2 -a2c2d2 -abcd3 -ac|
|  ac3d  0      0     ac3d    ac2d2  0       0      ac2d2   acd3    0      0  |
|  abc3  -ac4   -ac3d a2c2d   abc2d  -ac3d   -ac2d2 a2cd2   abcd2   -ac2d2 -ac|
|  0     a2c3   abc3  0       0      a2c2d   abc2d  0       0       a2cd2  abc|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|, 3}                                                                         |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0   c2d2 0    0    0    cd3 0   0   0   d4 0  0  0  |, {2} | -a2b2 -a3c -a2b|
| 0   0    c2d2 0    0    0   cd3 0   0   0  d4 0  0  |  {3} | a2c   a2d  0   |
| 0   0    0    c2d2 0    0   0   cd3 0   0  0  d4 0  |  {3} | a3    a2b  -a2c|
| c3d 0    0    0    c2d2 0   0   0   cd3 0  0  0  d4 |  {3} | 0     0    a3  |
|                                                                             |
|0    0    0    abd2 0    0    0    ac3 0   0   0   ac2d 0    0    0    acd2 0|
|abcd 0    0    0    abd2 0    0    0   ac3 0   0   0    ac2d 0    0    0    a|
|0    abcd 0    0    0    abd2 0    0   0   ac3 0   0    0    ac2d 0    0    0|
|0    0    abcd 0    0    0    abd2 0   0   0   ac3 0    0    0    ac2d 0    0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|cd-a3c2d a2c3d-ab2cd2 ac4d-abcd3 abcd2-a2d3 ab3d2-a3cd2 a2c2d2-ab2d3 ac3d2-ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-ab4 -a2b2c -ab3d -ab2c2 -ab3c -a2bc2 -ab2cd -abc3 -ab3d -a2bcd -ab2d2 -abc2d|
|ab2c ab2d   0     0      abc2  abcd   0      0     abcd  abd2   0      0     |
|a2b2 ab3    -ab2c -ab2d  a2bc  ab2c   -abc2  -abcd a2bd  ab2d   -abcd  -abd2 |
|0    0      a2b2  ab3    0     0      a2bc   ab2c  0     0      a2bd   ab2d  |
|-----------------------------------------------------------------------------|
|2 b3c3d-a2c4d ac5d-b2c3d2 c6d-bc3d3 bc3d2-ac2d3 b3c2d2-a2c3d2 ac4d2-b2c2d3 c5|
|                                                                             |
|                                                                             |
|3d2 -ab2d3 -a2cd3 -abd4 -ac2d3 -b6 -ab4c -b5d -b4c2 -b5c -ab3c2 -b4cd -b3c3 -|
|    acd3   ad4    0     0      b4c b4d   0    0     b3c2 b3cd   0     0     b|
|d3  a2d3   abd3   -acd3 -ad4   ab4 b5    -b4c -b4d  ab3c b4c    -b3c2 -b3cd a|
|d2  0      0      a2d3  abd3   0   0     ab4  b5    0    0      ab3c  b4c   0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|d -a2c2 -ab3 -a2bc -ab2d -abc2 -ab2c -a2c2 -abcd -ac3 -ab2d -a2cd -abd2 -ac2d|
|  0     abc  abd   0     0     ac2   acd   0     0    acd   ad2   0     0    |
|  -a2d  a2b  ab2   -abc  -abd  a2c   abc   -ac2  -acd a2d   abd   -acd  -ad2 |
|  a2b   0    0     a2b   ab2   0     0     a2c   abc  0     0     a2d   abd  |
|                                                                             |
|    0    0    ad3 0   0   0   b4 0  0  0  b3c 0   0   0   b3d 0   0   0   b2c|
|cd2 0    0    0   ad3 0   0   0  b4 0  0  0   b3c 0   0   0   b3d 0   0   0  |
|    acd2 0    0   0   ad3 0   0  0  b4 0  0   0   b3c 0   0   0   b3d 0   0  |
|    0    acd2 0   0   0   ad3 0  0  0  b4 0   0   0   b3c 0   0   0   b3d 0  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|d4 b4c-ab3d b6-a2b3c ab3c2-b5d b3c3-b4d2 b3c2-ab2cd b5c-a2b2c2 ab2c3-b4cd b2c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| -ab2c2 -a2c3 -abc2d -ac4  -ab2cd -a2c2d -abcd2 -ac3d -ab2d2 -a2cd2 -abd3 -ac|
| ac3    ac2d  0      0     ac2d   acd2   0      0     acd2   ad3    0     0  |
| a2c2   abc2  -ac3   -ac2d a2cd   abcd   -ac2d  -acd2 a2d2   abd2   -acd2 -ad|
| 0      0     a2c2   abc2  0      0      a2cd   abcd  0      0      a2d2  abd|
|-----------------------------------------------------------------------------|
|d2-bc2d4 bc2d3-acd4 b3cd3-a2c2d3 ac3d3-b2cd4 c4d3-bcd5 bcd4-ad5 b3d4-a2cd4 ac|
|                                                                             |
|                                                                             |
|b5d -ab3cd -b4d2 -b3c2d -b4c2 -ab2c3 -b3c2d -b2c4  -b4cd -ab2c2d -b3cd2 -b2c3|
|3cd b3d2   0     0      b2c3  b2c2d  0      0      b2c2d b2cd2   0      0    |
|b3d b4d    -b3cd -b3d2  ab2c2 b3c2   -b2c3  -b2c2d ab2cd b3cd    -b2c2d -b2cd|
|    0      ab3d  b4d    0     0      ab2c2  b3c2   0     0       ab2cd  b3cd |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| -b4 -ab2c -b3d -b2c2 -b3c -abc2 -b2cd -bc3 -b3d -abcd -b2d2 -bc2d -b2c2 -ac3|
| b2c b2d   0    0     bc2  bcd   0     0    bcd  bd2   0     0     c3    c2d |
| ab2 b3    -b2c -b2d  abc  b2c   -bc2  -bcd abd  b2d   -bcd  -bd2  ac2   bc2 |
| 0   0     ab2  b3    0    0     abc   b2c  0    0     abd   b2d   0     0   |
|                                                                             |
|2 0    0    0    b2cd 0    0    0    b2d2 0    0    0    bc3 0   0   0   bc2d|
|  b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0   bc3 0   0   0   |
|  0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0   0   bc3 0   0   |
|  0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0   0   0   bc3 0   |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|4-b3cd2 b3cd-ab2d2 b5d-a2b2cd ab2c2d-b4d2 b2c3d-b3d3 b2c3-abc2d b4c2-a2bc3 ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2d2 -b5 -ab3c -b4d -b3c2 -b4c -ab2c2 -b3cd -b2c3 -b4d -ab2cd -b3d2 -b2c2d -b3|
|    b3c b3d   0    0     b2c2 b2cd   0     0     b2cd b2d2   0     0      bc3|
|3   ab3 b4    -b3c -b3d  ab2c b3c    -b2c2 -b2cd ab2d b3d    -b2cd -b2d2  abc|
|2   0   0     ab3  b4    0    0      ab2c  b3c   0    0      ab2d  b3d    0  |
|-----------------------------------------------------------------------------|
|2d4-b2d5 c3d4-bd6 0 |, | a4bc-a5d a4b3-a6c a5c2-a4b2d a4c3-a4bd2 a3b2c-a4bd a|
|                                                                             |
|                                                                             |
|d -b4d2 -ab2cd2 -b3d3  -b2c2d2 -b3c3 -abc4 -b2c3d -bc5  -b3c2d -abc3d -b2c2d2|
|  b2cd2 b2d3    0      0       bc4   bc3d  0      0     bc3d   bc2d2  0      |
|2 ab2d2 b3d2    -b2cd2 -b2d3   abc3  b2c3  -bc4   -bc3d abc2d  b2c2d  -bc3d  |
|  0     0       ab2d2  b3d2    0     0     abc3   b2c3  0      0      abc2d  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| -bc2d -c4  -b2cd -ac2d -bcd2 -c3d -b2d2 -acd2 -bd3 -c2d2 a4 0  0  0  a3b 0  |
| 0     0    c2d   cd2   0     0    cd2   d3    0    0     0  a4 0  0  0   a3b|
| -c3   -c2d acd   bcd   -c2d  -cd2 ad2   bd2   -cd2 -d3   0  0  a4 0  0   0  |
| ac2   bc2  0     0     acd   bcd  0     0     ad2  bd2   0  0  0  a4 0   0  |
|                                                                             |
| 0    0    0    bcd2 0    0    0    bd3 0   0   0   c4 0  0  0  c3d 0   0   0|
| bc2d 0    0    0    bcd2 0    0    0   bd3 0   0   0  c4 0  0  0   c3d 0   0|
| 0    bc2d 0    0    0    bcd2 0    0   0   bd3 0   0  0  c4 0  0   0   c3d 0|
| 0    0    bc2d 0    0    0    bcd2 0   0   0   bd3 0  0  0  c4 0   0   0   c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|c4-b3c2d bc5-b2c2d2 b2c2d-abcd2 b4cd-a2bc2d abc3d-b3cd2 bc4d-b2cd3 b2cd2-abd3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|c2 -abc3 -b2c2d -bc4  -b3cd -abc2d -b2cd2 -bc3d -b3d2 -abcd2 -b2d3 -bc2d2 -b2|
|   bc2d  0      0     bc2d  bcd2   0      0     bcd2  bd3    0     0      c4 |
|2  b2c2  -bc3   -bc2d abcd  b2cd   -bc2d  -bcd2 abd2  b2d2   -bcd2 -bd3   ac3|
|   0     abc2   b2c2  0     0      abcd   b2cd  0     0      abd2  b2d2   0  |
|-----------------------------------------------------------------------------|
|3b4-a5bc a4bc2-a3b3d a3bc3-a3b2d2 a3bc2-a4cd a3b3c-a5c2 a4c3-a3b2cd a3c4-a3bc|
|                                                                             |
|                                                                             |
| -bc4d  -b3cd2 -abc2d2 -b2cd3 -bc3d2 -b3d3 -abcd3 -b2d4 -bc2d3 -b2c4 -ac5 -bc|
| 0      bc2d2  bcd3    0      0      bcd3  bd4    0     0      c5    c4d  0  |
| -bc2d2 abcd2  b2cd2   -bc2d2 -bcd3  abd3  b2d3   -bcd3 -bd4   ac4   bc4  -c5|
| b2c2d  0      0       abcd2  b2cd2  0     0      abd3  b2d3   0     0    ac4|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0   0   a3c 0   0   0   a3d 0   0   0   a2b2 0    0    0    a2bc 0    0    0|
| 0   0   0   a3c 0   0   0   a3d 0   0   0    a2b2 0    0    0    a2bc 0    0|
| a3b 0   0   0   a3c 0   0   0   a3d 0   0    0    a2b2 0    0    0    a2bc 0|
| 0   a3b 0   0   0   a3c 0   0   0   a3d 0    0    0    a2b2 0    0    0    a|
|                                                                             |
|   c2d2 0    0    0    cd3 0   0   0   d4 0  0  0  |) <----- 0 : {-3, 5}     |
|   0    c2d2 0    0    0   cd3 0   0   0  d4 0  0  |     0                   |
|   0    0    c2d2 0    0   0   cd3 0   0  0  d4 0  |                         |
|3d 0    0    0    c2d2 0   0   0   cd3 0  0  0  d4 |                         |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| b4d2-a2bcd2 abc2d2-b3d3 bc3d2-b2d4 bc4-ac3d b3c3-a2c4 ac5-b2c3d c6-bc3d2 bc3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|c3 -ac4 -bc3d -c5  -b2c2d -ac3d -bc2d2 -c4d  -b2cd2 -ac2d2 -bcd3 -c3d2 -b2d3 |
|   c3d  0     0    c3d    c2d2  0      0     c2d2   cd3    0     0     cd3   |
|   bc3  -c4   -c3d ac2d   bc2d  -c3d   -c2d2 acd2   bcd2   -c2d2 -cd3  ad3   |
|   0    ac3   bc3  0      0     ac2d   bc2d  0      0      acd2  bcd2  0     |
|-----------------------------------------------------------------------------|
|d2 a3bcd-a4d2 a3b3d-a5cd a4c2d-a3b2d2 a3c3d-a3bd3 a2b3c-a3b2d a2b5-a4b2c a3b2|
|                                                                             |
|                                                                             |
|4d -c6  -b2c3d -ac4d -bc3d2 -c5d  -b2c2d2 -ac3d2 -bc2d3 -c4d2 -b2cd3 -ac2d3 -|
|   0    c4d    c3d2  0      0     c3d2    c2d3   0      0     c2d3   cd4    0|
|   -c4d ac3d   bc3d  -c4d   -c3d2 ac2d2   bc2d2  -c3d2  -c2d3 acd3   bcd3   -|
|   bc4  0      0     ac3d   bc3d  0       0      ac2d2  bc2d2 0      0      a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0  |
|    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0  |
|    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d|
|2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|d-ac2d2 b3c2d-a2c3d ac4d-b2c2d2 c5d-bc2d3 bc2d2-acd3 b3cd2-a2c2d2 ac3d2-b2cd3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-acd3 -bd4 -c2d3 0 0 0 0 |, {2} | -a3b2 -a4c -a3bd -a3c2 -a2b3 -a3bc -a2b2d -|
|d4    0    0     0 0 0 0 |  {3} | a3c   a3d  0     0     a2bc  a2bd  0      0|
|bd3   -cd3 -d4   0 0 0 0 |  {3} | a4    a3b  -a3c  -a3d  a3b   a2b2  -a2bc  -|
|0     ad3  bd3   0 0 0 0 |  {3} | 0     0    a4    a3b   0     0     a3b    a|
|-----------------------------------------------------------------------------|
|c2-a2b4d a2b2c3-a2b3d2 a2b2c2-a3bcd a2b4c-a4bc2 a3bc3-a2b3cd a2bc4-a2b2cd2 a2|
|                                                                             |
|                                                                             |
|bcd4 -c3d3 -b2d4 -acd4 -bd5 -c2d4 0 0 0 0 |) <----- 0 : {-5, 6}              |
|     0     cd4   d5    0    0     0 0 0 0 |     0                            |
|c2d3 -cd4  ad4   bd4   -cd4 -d5   0 0 0 0 |                                  |
|cd3  bcd3  0     0     ad4  bd4   0 0 0 0 |                                  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|  0    ab3 0   0   0   ab2c 0    0    0    ab2d 0    0    0    abc2 0    0   |
|  0    0   ab3 0   0   0    ab2c 0    0    0    ab2d 0    0    0    abc2 0   |
|2 0    0   0   ab3 0   0    0    ab2c 0    0    0    ab2d 0    0    0    abc2|
|  a2d2 0   0   0   ab3 0    0    0    ab2c 0    0    0    ab2d 0    0    0   |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| c4d2-bcd4 bcd3-ad4 b3d3-a2cd3 ac2d3-b2d4 c3d3-bd5 0 |) <--------------------|
|                                                           {4} | 1 0 0 0 0 0 |
|                                                           {4} | 0 1 0 0 0 0 |
|                                                           {4} | 0 0 1 0 0 0 |
|                                                           {4} | 0 0 0 1 0 0 |
|                                                           {4} | 0 0 0 0 1 0 |
|                                                           {4} | 0 0 0 0 0 1 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {0} | 0 0 0 0 0 0 |
|                                                                             |
|a2bc2 -a2b2c -a3c2 -a2bcd -a2c3 -a2b2d -a3cd -a2bd2 -a2c2d -ab4 -a2b2c -ab3d |
|      a2c2   a2cd  0      0     a2cd   a2d2  0      0      ab2c ab2d   0     |
|a2bd  a3c    a2bc  -a2c2  -a2cd a3d    a2bd  -a2cd  -a2d2  a2b2 ab3    -ab2c |
|2b2   0      0     a3c    a2bc  0      0     a3d    a2bd   0    0      a2b2  |
|-----------------------------------------------------------------------------|
|b2cd-a3bd2 a2b4d-a4bcd a3bc2d-a2b3d2 a2bc3d-a2b2d3 a2bc3-a3c2d a2b3c2-a4c3 a3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0    abcd 0    0    0    abd2 0    0    0    ac3 0   0   0   ac2d 0    0    |
| 0    0    abcd 0    0    0    abd2 0    0    0   ac3 0   0   0    ac2d 0    |
| 0    0    0    abcd 0    0    0    abd2 0    0   0   ac3 0   0    0    ac2d |
| abc2 0    0    0    abcd 0    0    0    abd2 0   0   0   ac3 0    0    0    |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|------------------------------------------------------------- cokernel {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|                                                                             |
|-ab2c2 -ab3c -a2bc2 -ab2cd -abc3 -ab3d -a2bcd -ab2d2 -abc2d -ab2c2 -a2c3 -abc|
|0      abc2  abcd   0      0     abcd  abd2   0      0      ac3    ac2d  0   |
|-ab2d  a2bc  ab2c   -abc2  -abcd a2bd  ab2d   -abcd  -abd2  a2c2   abc2  -ac3|
|ab3    0     0      a2bc   ab2c  0     0      a2bd   ab2d   0      0     a2c2|
|-----------------------------------------------------------------------------|
|c4-a2b2c2d a2c5-a2bc2d2 a2bc2d-a3cd2 a2b3cd-a4c2d a3c3d-a2b2cd2 a2c4d-a2bcd3 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0    acd2 0    0    0    ad3 0   0   0   b4 0  0  0  b3c 0   0   0   b3d 0   |
|0    0    acd2 0    0    0   ad3 0   0   0  b4 0  0  0   b3c 0   0   0   b3d |
|0    0    0    acd2 0    0   0   ad3 0   0  0  b4 0  0   0   b3c 0   0   0   |
|ac2d 0    0    0    acd2 0   0   0   ad3 0  0  0  b4 0   0   0   b3c 0   0   |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-d -b -d -c 0  0  -d 0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0 |
|c  a  0  0  0  -d 0  -d -b 0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0 |
|0  0  b  a  -d 0  0  0  0  0  -d 0  0  0  0  0  -d -c 0  0  -d 0  0  0  0  0 |
|0  0  0  0  c  b  a  0  0  -d 0  0  0  -d 0  0  0  0  0  -d 0  0  0  -d 0  0 |
|0  0  0  0  0  0  0  c  a  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  -d -b|
|0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  0  0  0  0  0  0  -d 0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  b  a  -d 0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  -d 0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  a |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2d -ac4  -ab2cd -a2c2d -abcd2 -ac3d -ab2d2 -a2cd2 -abd3 -ac2d2 -b5 -ab3c -b4d|
|   0     ac2d   acd2   0      0     acd2   ad3    0     0      b3c b3d   0   |
|   -ac2d a2cd   abcd   -ac2d  -acd2 a2d2   abd2   -acd2 -ad3   ab3 b4    -b3c|
|   abc2  0      0      a2cd   abcd  0      0      a2d2  abd2   0   0     ab3 |
|-----------------------------------------------------------------------------|
|a2bcd2-a3d3 a2b3d2-a4cd2 a3c2d2-a2b2d3 a2c3d2-a2bd4 ab4c-a2b3d ab6-          |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0   0   b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0             |
|0   0   0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0             |
|b3d 0   0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0             |
|0   b3d 0    0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2          |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0            |
| 0  -d 0  0  0  0  0  0  0  -d 0  0  0  0  -d 0  0  0  0  0  0  0            |
| 0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| -d 0  0  0  -d 0  0  0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0            |
| 0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  -d -c 0  0            |
| 0  0  0  0  0  0  0  -d 0  0  0  0  -d 0  0  0  0  0  0  0  0  -d           |
| 0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0  0  0            |
| 0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| d  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  c  b  a  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0            |
| 0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  b  a  -d 0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| -b3c2 -b4c -ab2c2 -b3cd -b2c3 -b4d -ab2cd -b3d2 -b2c2d -b3c2 -abc3          |
| 0     b2c2 b2cd   0     0     b2cd b2d2   0     0      bc3   bc2d           |
| -b3d  ab2c b3c    -b2c2 -b2cd ab2d b3d    -b2cd -b2d2  abc2  b2c2           |
| b4    0    0      ab2c  b3c   0    0      ab2d  b3d    0     0              |
|-----------------------------------------------------------------------------|
|a3b3c a2b3c2-ab5d ab3c3-ab4d2 ab3c2-a2b2cd ab5c-a3b2c2 a2b2c3-ab4cd ab2c4-ab3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| bc3 0   0   0   bc2d 0    0    0    bcd2 0    0    0    bd3 0   0   0   c4 0|
| 0   bc3 0   0   0    bc2d 0    0    0    bcd2 0    0    0   bd3 0   0   0  c|
| 0   0   bc3 0   0    0    bc2d 0    0    0    bcd2 0    0   0   bd3 0   0  0|
| 0   0   0   bc3 0    0    0    bc2d 0    0    0    bcd2 0   0   0   bd3 0  0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  -d 0  0  0  0  -d 0  0 |
|-d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  0 |
|0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  -d 0  0  0  0  -d 0  0  0  0 |
|0  0  0  0  0  0  0  -d -b 0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  -d 0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  -d 0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|a  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  c  b  a  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  c  a  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  0  0  0  0  0  0  0  0  0  -d|
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  d  c  b  a  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| -b2c2d -bc4  -b3cd -abc2d -b2cd2 -bc3d -b3d2 -abcd2 -b2d3 -bc2d2 -b2c3 -ac4 |
| 0      0     bc2d  bcd2   0      0     bcd2  bd3    0     0      c4    c3d  |
| -bc3   -bc2d abcd  b2cd   -bc2d  -bcd2 abd2  b2d2   -bcd2 -bd3   ac3   bc3  |
| abc2   b2c2  0     0      abcd   b2cd  0     0      abd2  b2d2   0     0    |
|-----------------------------------------------------------------------------|
|cd2 ab3cd-a2b2d2 ab5d-a3b2cd a2b2c2d-ab4d2 ab2c3d-ab3d3 ab2c3-a2bc2d ab4c2-  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|  0  0  c3d 0   0   0   c2d2 0    0    0    cd3 0   0   0   d4 0  0  0  |)   |
|4 0  0  0   c3d 0   0   0    c2d2 0    0    0   cd3 0   0   0  d4 0  0  |    |
|  c4 0  0   0   c3d 0   0    0    c2d2 0    0   0   cd3 0   0  0  d4 0  |    |
|  0  c4 0   0   0   c3d 0    0    0    c2d2 0   0   0   cd3 0  0  0  d4 |    |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  -d 0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  -d 0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0   |
| 0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  -d -c 0  0  -d 0  0  0  0   |
| 0  -d 0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  -d 0   |
| 0  0  0  0  0  -d 0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  -d 0  0   |
| 0  0  0  0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| a  0  0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0   |
| 0  d  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  b  a  -d 0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  -d 0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  -d  |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-bc3d -c5  -b2c2d -ac3d -bc2d2 -c4d  -b2cd2 -ac2d2 -bcd3 -c3d2 -b2d3 -acd3   |
|0     0    c3d    c2d2  0      0     c2d2   cd3    0     0     cd3   d4      |
|-c4   -c3d ac2d   bc2d  -c3d   -c2d2 acd2   bcd2   -c2d2 -cd3  ad3   bd3     |
|ac3   bc3  0      0     ac2d   bc2d  0      0      acd2  bcd2  0     0       |
|-----------------------------------------------------------------------------|
|a3bc3 a2bc4-ab3c2d abc5-ab2c2d2 ab2c2d-a2bcd2 ab4cd-a3bc2d a2bc3d-ab3cd2     |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|<----- 0 : {-3, 4}                                                           |
|   0                                                                         |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0  0  0  0  0  c2  -ac 0   0   -cd -ad 0   0   0   -d2 -bd 0   0   0        |
| 0  0  0  0  0  -bd b2  -d2 0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   c2  cd  0   0   0   0   -d2 0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   -d2 0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   -d2 bd  b2  0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   -d2 0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   cd  c2  0   0   0   -d2 0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   -d2      |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   d2  bd  b2  0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   d2  0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   -d2 0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   d2  cd       |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  -d 0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| -d 0  0  0  -d 0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  -d 0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| b  a  -d 0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  c  b  a  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-bd4 -c2d3 0 0 0 0 |) <----- 0 : {-4, 5}                                     |
|0    0     0 0 0 0 |     0                                                   |
|-cd3 -d4   0 0 0 0 |                                                         |
|ad3  bd3   0 0 0 0 |                                                         |
|-----------------------------------------------------------------------------|
| abc4d-ab2cd3 ab2cd2-a2bd3 ab4d2-a3bcd2 a2bc2d2-ab3d3 abc3d2-ab2d4 abc4-a2c3d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0   0   0   0   0   0   0   0   0   0   | : {-4, 4}                          |
|0   0   -d2 -bd 0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   -d2 0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|-d2 0   0   0   -d2 0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|c2  0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   -d2 0   0   -d2 0   |                                    |
|0   0   0   0   0   0   0   -d2 0   0   |                                    |
|0   0   0   0   0   0   -d2 0   0   0   |                                    |
|0   d2  bd  b2  0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   d2  0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   d2  0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   -d2 |                                    |
|0   0   0   0   0   0   d2  cd  c2  0   |                                    |
|0   0   0   0   0   0   0   0   0   d2  |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|-----------------------------------------------------------------------------|
|ab3c3-a3c4 a2c5-ab2c3d ac6-abc3d2 abc3d-a2c2d2 ab3c2d-a3c3d a2c4d-ab2c2d2    |
|                                                                             |
|-----------------------------------------------------------------------------|
|ac5d-abc2d3 abc2d2-a2cd3 ab3cd2-a3c2d2 a2c3d2-ab2cd3 ac4d2-abcd4 abcd3-a2d4  |
|                                                                             |
|-----------------------------------------------------------------------------|
|ab3d3-a3cd3 a2c2d3-ab2d4 ac3d3-abd5 b5c-ab4d b7-a2b4c ab4c2-b6d b4c3-b5d2    |
|                                                                             |
|-----------------------------------------------------------------------------|
|b4c2-ab3cd b6c-a2b3c2 ab3c3-b5cd b3c4-b4cd2 b4cd-ab3d2 b6d-a2b3cd ab3c2d-b5d2|
|                                                                             |
|-----------------------------------------------------------------------------|
|b3c3d-b4d3 b3c3-ab2c2d b5c2-a2b2c3 ab2c4-b4c2d b2c5-b3c2d2 b3c2d-ab2cd2      |
|                                                                             |
|-----------------------------------------------------------------------------|
|b5cd-a2b2c2d ab2c3d-b4cd2 b2c4d-b3cd3 b3cd2-ab2d3 b5d2-a2b2cd2 ab2c2d2-b4d3  |
|                                                                             |
|-----------------------------------------------------------------------------|
|b2c3d2-b3d4 b2c4-abc3d b4c3-a2bc4 abc5-b3c3d bc6-b2c3d2 b2c3d-abc2d2         |
|                                                                             |
|-----------------------------------------------------------------------------|
|b4c2d-a2bc3d abc4d-b3c2d2 bc5d-b2c2d3 b2c2d2-abcd3 b4cd2-a2bc2d2 abc3d2-b3cd3|
|                                                                             |
|-----------------------------------------------------------------------------|
|bc4d2-b2cd4 b2cd3-abd4 b4d3-a2bcd3 abc2d3-b3d4 bc3d3-b2d5 bc5-ac4d b3c4-a2c5 |
|                                                                             |
|-----------------------------------------------------------------------------|
|ac6-b2c4d c7-bc4d2 bc4d-ac3d2 b3c3d-a2c4d ac5d-b2c3d2 c6d-bc3d3 bc3d2-ac2d3  |
|                                                                             |
|-----------------------------------------------------------------------------|
|b3c2d2-a2c3d2 ac4d2-b2c2d3 c5d2-bc2d4 bc2d3-acd4 b3cd3-a2c2d3 ac3d3-b2cd4    |
|                                                                             |
|-----------------------------------------------------------------------------|
|c4d3-bcd5 bcd4-ad5 b3d4-a2cd4 ac2d4-b2d5 c3d4-bd6 0 |) <----- 0 : {-5, 5}    |
|                                                          0                  |
+-----------------------------------------------------------------------------+

See also
========

  * pruningMaps(SpectralSequencePage)
    -- compute the pruning maps on a
    spectral sequence page
  * prune (Macaulay2Doc) -- prune, e.g., compute a minimal
    presentation

Types of page map:
==================

  * SpectralSequencePageMap -- the type of all
    spectral sequence page maps

Methods that use a page map:
============================

  * describe(PageMap) -- real description
  * net(PageMap)
  * PageMap _ List
  * spots(PageMap)
  * support(PageMap)

For the programmer
==================

The object PageMap, is a type (Macaulay2Doc), with
ancestor classes MutableHashTable (Macaulay2Doc), <
HashTable (Macaulay2Doc) < Thing (Macaulay2Doc).

-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2556:0.

pageMap
*******

For the programmer
==================

The object pageMap, is a symbol (Macaulay2Doc).

-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2358:0.

PageMap _ List
**************

  * Operator: _ (Macaulay2Doc),

Ways to use this method:
========================

  * PageMap _ List
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2300:0.

pruningMaps -- compute the pruning maps on a spectral sequence page
*******************************************************************

  * Usage:
        d = pruningMaps E
  * Inputs:
      * E, a spectral sequence page,
  * Outputs:
      * d, a page map,

Description
===========

Returns the pruning maps which are cached in the process of pruning the
spectral sequence page.

As a specific example consider the filtered complex $K$ below, obtained by
multiplying the minimal free resolution of the rational quartic space curve by
successive powers of the irrelevant ideal.

+----------------------------------------------------+
|i1 : B = QQ[a..d];                                  |
+----------------------------------------------------+
|i2 : J = ideal vars B;                              |
|                                                    |
|o2 : Ideal of B                                     |
+----------------------------------------------------+
|i3 : C = complete res monomialCurveIdeal(B,{1,3,4});|
+----------------------------------------------------+
|i4 : K = filteredComplex(J,C,4);                    |
+----------------------------------------------------+

We compute an example of a pruning map below.

+-----------------------------------------------------------------------------+
|i5 : E = prune spectralSequence K;                                           |
+-----------------------------------------------------------------------------+
|i6 : pruningMaps E^2                                                         |
|                                                                             |
|o6 = {-7, 6} : subquotient (| 0 a4bc-a5d a4b3-a6c a5c2-a4b2d a4c3-a4bd2 a3b2c|
|                                                                             |
|                                                                             |
|     {-7, 7} : subquotient ({2} | 0 0 0 0 -a4b2 -a5c -a4bd -a4c2 -a3b3 -a4bc |
|                            {3} | 0 0 0 0 a4c   a4d  0     0     a3bc  a3bd  |
|                            {3} | 0 0 0 0 a5    a4b  -a4c  -a4d  a4b   a3b2  |
|                            {3} | 0 0 0 0 0     0    a5    a4b   0     0     |
|                                                                             |
|     {-7, 8} : subquotient ({4} | 0 0 0 0 a4d  a3bd  a3cd  a3d2  a2b2d  a2bcd|
|                            {4} | 0 0 0 0 -a4c -a3bc -a3c2 -a3cd -a2b2c -a2bc|
|                            {4} | 0 0 0 0 -a4b -a3b2 -a3bc -a3bd -a2b3  -a2b2|
|                            {4} | 0 0 0 0 a5   a4b   a4c   a4d   a3b2   a3bc |
|                                                                             |
|     {-7, 9} : image 0 <----- 0 : {-5, 8}                                    |
|                          0                                                  |
|                                                                             |
|     {-7, 10} : 0 <----- 0 : {-5, 9}                                         |
|                     0                                                       |
|                                                                             |
|     {-2, 1} : cokernel | bc-ad b3-a2c ac2-b2d c3-bd2 a b c d | <--------- co|
|                                                                   | 1 |     |
|                                                                             |
|     {-2, 2} : cokernel {2} | -b2 -ac -bd -c2 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0|
|                        {3} | c   d   0   0   0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0|
|                        {3} | a   b   -c  -d  0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0|
|                        {3} | 0   0   a   b   0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d|
|                                                                             |
|                                                                             |
|     {-2, 3} : subquotient ({4} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 d  a 0 0 0 |
|                            {4} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 -c 0 a 0 0 |
|                            {4} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 -b 0 0 a 0 |
|                            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a a  0 0 0 a |
|                                                                             |
|     {-2, 4} : subquotient ({5} | d c b a a b c d |, {5} | a b c d |) <----- |
|                                                                         0   |
|                                                                             |
|     {-2, 5} : 0 <----- 0 : {0, 4}                                           |
|                    0                                                        |
|                                                                             |
|     {-3, 2} : subquotient (| a b c d bc-ad b3-a2c ac2-b2d c3-bd2 a2 ab ac ad|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|     {-3, 3} : subquotient ({2} | a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 -b2 -ac -bd|
|                            {3} | 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 c   d   0  |
|                            {3} | 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 a   b   -c |
|                            {3} | 0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0   0   a  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|     {-3, 4} : subquotient ({4} | d  ad ac ab a2 0  0  0  0  0  0  0  0  0  0|
|                            {4} | -c 0  0  0  0  ad ac ab a2 0  0  0  0  0  0|
|                            {4} | -b 0  0  0  0  0  0  0  0  ad ac ab a2 0  0|
|                            {4} | a  0  0  0  0  0  0  0  0  0  0  0  0  ad a|
|                                                                             |
|     {-3, 5} : subquotient ({5} | ad ac ab a2 bd bc b2 ab cd c2 bc ac d2 cd b|
|                                                                             |
|                                                                             |
|     {-3, 6} : 0 <----- 0 : {-1, 5}                                          |
|                    0                                                        |
|                                                                             |
|     {-4, 3} : subquotient (| a2 ab ac ad b2 bc bd c2 cd d2 abc-a2d ab3-a3c a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|     {-4, 4} : subquotient ({2} | a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0|
|                            {3} | 0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0|
|                            {3} | 0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  a|
|                            {3} | 0  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|     {-4, 5} : subquotient ({4} | ad  bd  cd  d2  a2d a2c a2b a3 0   0   0   |
|                            {4} | -ac -bc -c2 -cd 0   0   0   0  a2d a2c a2b |
|                            {4} | -ab -b2 -bc -bd 0   0   0   0  0   0   0   |
|                            {4} | a2  ab  ac  ad  0   0   0   0  0   0   0   |
|                                                                             |
|     {-4, 6} : subquotient ({5} | a2d a2c a2b a3 abd abc ab2 a2b acd ac2 abc |
|                                                                             |
|                                                                             |
|     {-4, 7} : 0 <----- 0 : {-2, 6}                                          |
|                    0                                                        |
|                                                                             |
|     {-5, 4} : subquotient (| a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3 b2c b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|     {-5, 5} : subquotient ({2} | 0 a2b2 a2bd a2bd 0 a3c  a3c  a2c2 a2b2 ab3 |
|                            {3} | 0 -a2c 0    0    0 -a2d -a2d 0    -a2c -abc|
|                            {3} | 0 -a3  a2c  a2c  0 -a2b -a2b a2d  -a3  -a2b|
|                            {3} | 0 0    -a3  -a3  0 0    0    -a2b 0    0   |
|                                                                             |
|     {-5, 6} : subquotient ({4} | a2d  abd  acd  ad2  b2d  bcd  bd2  c2d  cd2|
|                            {4} | -a2c -abc -ac2 -acd -b2c -bc2 -bcd -c3  -c2|
|                            {4} | -a2b -ab2 -abc -abd -b3  -b2c -b2d -bc2 -bc|
|                            {4} | a3   a2b  a2c  a2d  ab2  abc  abd  ac2  acd|
|                                                                             |
|     {-5, 7} : subquotient ({5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                                                                             |
|                                                                             |
|     {-5, 8} : 0 <----- 0 : {-3, 7}                                          |
|                    0                                                        |
|                                                                             |
|     {-6, 5} : subquotient (| a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|     {-6, 6} : subquotient ({2} | 0 a3b2 a3bd a3bd 0 a4c  a4c  a3c2 a3b2 a2b3|
|                            {3} | 0 -a3c 0    0    0 -a3d -a3d 0    -a3c -a2b|
|                            {3} | 0 -a4  a3c  a3c  0 -a3b -a3b a3d  -a4  -a3b|
|                            {3} | 0 0    -a4  -a4  0 0    0    -a3b 0    0   |
|                                                                             |
|     {-6, 7} : subquotient ({4} | a3d  a2bd  a2cd  a2d2  ab2d  abcd  abd2  ac|
|                            {4} | -a3c -a2bc -a2c2 -a2cd -ab2c -abc2 -abcd -a|
|                            {4} | -a3b -a2b2 -a2bc -a2bd -ab3  -ab2c -ab2d -a|
|                            {4} | a4   a3b   a3c   a3d   a2b2  a2bc  a2bd  a2|
|                                                                             |
|     {-6, 8} : image 0 <----- 0 : {-4, 7}                                    |
|                          0                                                  |
|                                                                             |
|     {-6, 9} : 0 <----- 0 : {-4, 8}                                          |
|                    0                                                        |
|                                                                             |
|o6 : PageMap                                                                 |
|-----------------------------------------------------------------------------|
|-a4bd a3b4-a5bc a4bc2-a3b3d a3bc3-a3b2d2 a3bc2-a4cd a3b3c-a5c2 a4c3-a3b2cd a3|
|                                                                             |
|                                                                             |
|-a3b2d -a3bc2 -a3b2c -a4c2 -a3bcd -a3c3 -a3b2d -a4cd -a3bd2 -a3c2d -a2b4 -a3b|
|0      0      a3c2   a3cd  0      0     a3cd   a3d2  0      0      a2b2c a2b2|
|-a3bc  -a3bd  a4c    a3bc  -a3c2  -a3cd a4d    a3bd  -a3cd  -a3d2  a3b2  a2b3|
|a4b    a3b2   0      0     a4c    a3bc  0      0     a4d    a3bd   0     0   |
|                                                                             |
|  a2bd2  a2c2d  a2cd2  a2d3   ab3d  ab2cd  ab2d2  abc2d  abcd2  abd3   ac3d  |
|2 -a2bcd -a2c3  -a2c2d -a2cd2 -ab3c -ab2c2 -ab2cd -abc3  -abc2d -abcd2 -ac4  |
|c -a2b2d -a2bc2 -a2bcd -a2bd2 -ab4  -ab3c  -ab3d  -ab2c2 -ab2cd -ab2d2 -abc3 |
|  a3bd   a3c2   a3cd   a3d2   a2b3  a2b2c  a2b2d  a2bc2  a2bcd  a2bd2  a2c3  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|kernel | d c b a | : {0, 0}                                                  |
|                                                                             |
|                                                                             |
| | <------------------- cokernel {2} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 | : {0|
| |    {2} | 1 0 0 0 |            {3} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 |     |
| |    {3} | 0 1 0 0 |            {3} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 |     |
| |    {3} | 0 0 1 0 |            {3} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a |     |
|      {3} | 0 0 0 1 |                                                        |
|                                                                             |
|b 0 0 0 c 0 0 0 d 0 0 0 |, {4} | d  a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 |) <-----|
|0 b 0 0 0 c 0 0 0 d 0 0 |  {4} | -c 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 |     0  |
|0 0 b 0 0 0 c 0 0 0 d 0 |  {4} | -b 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 |        |
|0 0 0 b 0 0 0 c 0 0 0 d |  {4} | a  0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d |        |
|                                                                             |
|0 : {0, 3}                                                                   |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| b2 bc bd c2 cd d2 |, | bc-ad b3-a2c ac2-b2d c3-bd2 a2 ab ac ad b2 bc bd c2 c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| -c2 a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  |
| 0   0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  |
| -d  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  |
| b   0  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|  0  0  bd bc b2 ab 0  0  0  0  0  0  0  0  0  0  0  0  cd c2 bc ac 0  0  0  |
|  0  0  0  0  0  0  bd bc b2 ab 0  0  0  0  0  0  0  0  0  0  0  0  cd c2 bc |
|  0  0  0  0  0  0  0  0  0  0  bd bc b2 ab 0  0  0  0  0  0  0  0  0  0  0  |
|c ab a2 0  0  0  0  0  0  0  0  0  0  0  0  bd bc b2 ab 0  0  0  0  0  0  0  |
|                                                                             |
|d ad a2 ab ac ad b2 bc bd c2 cd d2 |, {5} | a2 ab ac ad b2 bc bd c2 cd d2 |) |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2c2-ab2d ac3-abd2 b2c-abd b4-a2bc abc2-b3d bc3-b2d2 bc2-acd b3c-a2c2 ac3-b2cd|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |
|  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |
|d 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |
|  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0  0   0   0   0  0   0   0   0  abd abc ab2 a2b 0   0   0   0   0   0   0   |
|a3 0   0   0   0  0   0   0   0  0   0   0   0   abd abc ab2 a2b 0   0   0   |
|0  a2d a2c a2b a3 0   0   0   0  0   0   0   0   0   0   0   0   abd abc ab2 |
|0  0   0   0   0  a2d a2c a2b a3 0   0   0   0   0   0   0   0   0   0   0   |
|                                                                             |
|a2c ad2 acd abd a2d b2d b2c b3 ab2 bcd bc2 b2c abc bd2 bcd b2d abd c2d c3 bc2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2d bc2 bcd bd2 c3 c2d cd2 d3 a2bc-a3d a2b3-a4c a3c2-a2b2d a2c3-a2bd2 ab2c-a2b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| ab2d ab2d a2bd a2bc a2bc a2bc abc2 abc2 a2c2 ab2c ab2c abcd abcd abcd 0     |
| 0    0    0    -abd -abd -abd 0    0    0    -ac2 -ac2 0    0    0    acd   |
| abc  abc  a2c  -ab2 -ab2 -ab2 abd  abd  a2d  -a2c -a2c ac2  ac2  ac2  abc+a2|
| -a2b -a2b -a3  0    0    0    -ab2 -ab2 -a2b 0    0    -a2c -a2c -a2c -a2b  |
|                                                                             |
|  d3   a3d  0 0 -a2bd 0 0 0 0 -a2cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -ab2d -|
|d -cd2 -a3c 0 0 a2bc  0 0 0 0 a2c2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ab2c  a|
|d -bd2 -a3b 0 0 a2b2  0 0 0 0 a2bc  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ab3   a|
|  ad2  a4   0 0 -a3b  0 0 0 0 -a3c  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a2b2 -|
|                                                                             |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a4 a3b a3c a3d a2b2 a2bc a2bd |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|3 ab2c ab2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|  a2b2d a2b2d a3bd a3bc  a3bc  a3bc  a2bc2 a2bc2 a3c2 a2b2c a2b2c a2bcd a2bcd|
|c 0     0     0    -a2bd -a2bd -a2bd 0     0     0    -a2c2 -a2c2 0     0    |
|  a2bc  a2bc  a3c  -a2b2 -a2b2 -a2b2 a2bd  a2bd  a3d  -a3c  -a3c  a2c2  a2c2 |
|  -a3b  -a3b  -a4  0     0     0     -a2b2 -a2b2 -a3b 0     0     -a3c  -a3c |
|                                                                             |
|2d  acd2  ad3   b3d  b2cd  b2d2  bc2d  bcd2  bd3   c3d  c2d2  cd3   d4   a4d |
|c3  -ac2d -acd2 -b3c -b2c2 -b2cd -bc3  -bc2d -bcd2 -c4  -c3d  -c2d2 -cd3 -a4c|
|bc2 -abcd -abd2 -b4  -b3c  -b3d  -b2c2 -b2cd -b2d2 -bc3 -bc2d -bcd2 -bd3 -a4b|
|c2  a2cd  a2d2  ab3  ab2c  ab2d  abc2  abcd  abd2  ac3  ac2d  acd2  ad3  a5  |
|-----------------------------------------------------------------------------|
|c4-a3bcd2 a3bcd-a4d2 a3b3d-a5cd a4c2d-a3b2d2 a3c3d-a3bd3 a2b3c-a3b2d a2b5-a4b|
|                                                                             |
|                                                                             |
|2c -a2b3d -a2b2c2 -a2b3c -a3bc2 -a2b2cd -a2bc3 -a2b3d -a3bcd -a2b2d2 -a2bc2d |
|d  0      0       a2bc2  a2bcd  0       0      a2bcd  a2bd2  0       0       |
|   -a2b2c -a2b2d  a3bc   a2b2c  -a2bc2  -a2bcd a3bd   a2b2d  -a2bcd  -a2bd2  |
|   a3b2   a2b3    0      0      a3bc    a2b2c  0      0      a3bd    a2b2d   |
|                                                                             |
|ac2d2  acd3   ad4   b4d  b3cd  b3d2  b2c2d b2cd2  b2d3   bc3d  bc2d2  bcd3   |
|-ac3d  -ac2d2 -acd3 -b4c -b3c2 -b3cd -b2c3 -b2c2d -b2cd2 -bc4  -bc3d  -bc2d2 |
|-abc2d -abcd2 -abd3 -b5  -b4c  -b4d  -b3c2 -b3cd  -b3d2  -b2c3 -b2c2d -b2cd2 |
|a2c2d  a2cd2  a2d3  ab4  ab3c  ab3d  ab2c2 ab2cd  ab2d2  abc3  abc2d  abcd2  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|, 1}                                                                         |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0 : {0, 2}                                                                  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|d d2 |) <------------------- cokernel {1} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 ||
|           {1} | 1 0 0 0 |            {1} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 ||
|           {1} | 0 1 0 0 |            {1} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 ||
|           {1} | 0 0 1 0 |            {1} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a ||
|           {1} | 0 0 0 1 |                                                   |
|           {2} | 0 0 0 0 |                                                   |
|           {3} | 0 0 0 0 |                                                   |
|           {3} | 0 0 0 0 |                                                   |
|           {3} | 0 0 0 0 |                                                   |
|           {2} | 0 0 0 0 |                                                   |
|           {2} | 0 0 0 0 |                                                   |
|           {2} | 0 0 0 0 |                                                   |
|           {2} | 0 0 0 0 |                                                   |
|           {2} | 0 0 0 0 |                                                   |
|           {2} | 0 0 0 0 |                                                   |
|           {2} | 0 0 0 0 |                                                   |
|           {2} | 0 0 0 0 |                                                   |
|           {2} | 0 0 0 0 |                                                   |
|           {2} | 0 0 0 0 |                                                   |
|                                                                             |
|bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |, {2} | -b2 -ac -bd -c2 a2 0|
|0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |  {3} | c   d   0   0   0  a|
|0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |  {3} | a   b   -c  -d  0  0|
|0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |  {3} | 0   0   a   b   0  0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  d  a2 0  0  0 |
|ac 0  0  0  0  0  0  0  0  d2 cd bd ad 0  0  0  0  0  0  0  0  -c 0  a2 0  0 |
|0  cd c2 bc ac 0  0  0  0  0  0  0  0  d2 cd bd ad 0  0  0  0  -b 0  0  a2 0 |
|0  0  0  0  0  cd c2 bc ac 0  0  0  0  0  0  0  0  d2 cd bd ad a  0  0  0  a2|
|                                                                             |
|<----- 0 : {-1, 4}                                                           |
|   0                                                                         |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| c4-bcd2 bcd-ad2 b3d-a2cd ac2d-b2d2 c3d-bd3 a3 a2b a2c a2d ab2 abc abd ac2 ac|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-ab2 -a2c -abd -ac2 -b3 -abc -b2d -bc2 -b2c -ac2 -bcd -c3 -b2d -acd -bd2 -c2d|
|ac   ad   0    0    bc  bd   0    0    c2   cd   0    0   cd   d2   0    0   |
|a2   ab   -ac  -ad  ab  b2   -bc  -bd  ac   bc   -c2  -cd ad   bd   -cd  -d2 |
|0    0    a2   ab   0   0    ab   b2   0    0    ac   bc  0    0    ad   bd  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0   0   0   0   0   acd ac2 abc a2c 0   0   0   0   0   0   0   0   0   0   0|
|0   0   0   0   0   0   0   0   0   acd ac2 abc a2c 0   0   0   0   0   0   0|
|a2b 0   0   0   0   0   0   0   0   0   0   0   0   acd ac2 abc a2c 0   0   0|
|0   abd abc ab2 a2b 0   0   0   0   0   0   0   0   0   0   0   0   acd ac2 a|
|                                                                             |
| ac2 cd2 c2d bcd acd d3 cd2 bd2 ad2 a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|d ab4-a3bc a2bc2-ab3d abc3-ab2d2 abc2-a2cd ab3c-a3c2 a2c3-ab2cd ac4-abcd2 abc|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|  abd2 ac3  abd2 0 a2cd a2cd a2cd ac2d ac2d ab3  ab2c b4   b3d  b3d  ab2d 0  |
|  0    0    0    0 -ad2 -ad2 -ad2 0    0    -abc -ac2 -b2c 0    0    0    -ac|
|d acd  acd  acd  0 -abd -abd -abd ad2  ad2  -a2b -a2c -ab2 b2c  b2c  abc  b3-|
|  -a2d -abc -a2d 0 0    0    0    -abd -abd 0    0    0    -ab2 -ab2 -a2b 0  |
|                                                                             |
|a2bd 0 0 0 -abcd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -ac2d -abcd -a2cd 0 0 0 0 |
|2bc  0 0 0 abc2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ac3   abc2  a2c2  0 0 0 0 |
|2b2  0 0 0 ab2c  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 abc2  ab2c  a2bc  0 0 0 0 |
|a3b  0 0 0 -a2bc 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a2c2 -a2bc -a3c  0 0 0 0 |
|                                                                             |
|a2c2 a2cd a2d2 ab3 ab2c ab2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2d bcd2 bd3 c4 c3d c2d2 cd3 d4 a3bc-a4d a3b3-a5c a4c2-a3b2d a3c3-a3bd2 a2b2c-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| a2bcd 0        a2bd2 a2c3  a2bd2 0 a3cd  a3cd  a3cd  a2c2d a2c2d a2b3  a2b2c|
| 0     a2cd     0     0     0     0 -a2d2 -a2d2 -a2d2 0     0     -a2bc -a2c2|
| a2c2  a2bc+a3d a2cd  a2cd  a2cd  0 -a2bd -a2bd -a2bd a2d2  a2d2  -a3b  -a3c |
| -a3c  -a3b     -a3d  -a2bc -a3d  0 0     0     0     -a2bd -a2bd 0     0    |
|                                                                             |
| 0 0 -a3bd 0 0 0 0 -a3cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a2b2d -a3bd 0 0 0|
| 0 0 a3bc  0 0 0 0 a3c2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a2b2c  a3bc  0 0 0|
| 0 0 a3b2  0 0 0 0 a3bc  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a2b3   a3b2  0 0 0|
| 0 0 -a4b  0 0 0 0 -a4c  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a3b2  -a4b  0 0 0|
|-----------------------------------------------------------------------------|
|2c a3b2c2-a2b4d a2b2c3-a2b3d2 a2b2c2-a3bcd a2b4c-a4bc2 a3bc3-a2b3cd a2bc4-a2b|
|                                                                             |
|                                                                             |
|-a2b2c2 -a3c3 -a2bc2d -a2c4  -a2b2cd -a3c2d -a2bcd2 -a2c3d -a2b2d2 -a3cd2 -a2|
|a2c3    a2c2d 0       0      a2c2d   a2cd2  0       0      a2cd2   a2d3   0  |
|a3c2    a2bc2 -a2c3   -a2c2d a3cd    a2bcd  -a2c2d  -a2cd2 a3d2    a2bd2  -a2|
|0       0     a3c2    a2bc2  0       0      a3cd    a2bcd  0       0      a3d|
|                                                                             |
|bd4   c4d  c3d2  c2d3   cd4   d5   0 0 0 0 |, {4} | a4d  a3bd  a3cd  a3d2  a2|
|-bcd3 -c5  -c4d  -c3d2  -c2d3 -cd4 0 0 0 0 |  {4} | -a4c -a3bc -a3c2 -a3cd -a|
|-b2d3 -bc4 -bc3d -bc2d2 -bcd3 -bd4 0 0 0 0 |  {4} | -a4b -a3b2 -a3bc -a3bd -a|
|abd3  ac4  ac3d  ac2d2  acd3  ad4  0 0 0 0 |  {4} | a5   a4b   a4c   a4d   a3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| : {-1, 1}                                                                   |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  |
|2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  |
|  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd |
|  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0|
| 0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c|
| 0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0|
| 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|d ad2 b3 b2c b2d bc2 bcd bd2 c3 c2d cd2 d3 |, | abc-a2d ab3-a3c a2c2-ab2d ac3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   |
| 0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   |
| 0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   |
| 0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|   0   0   0   0   0   0   0   0   0   0   0   0   0   b2d b2c b3 ab2 0   0  |
|   0   ad2 acd abd a2d 0   0   0   0   0   0   0   0   0   0   0  0   b2d b2c|
|   0   0   0   0   0   ad2 acd abd a2d 0   0   0   0   0   0   0  0   0   0  |
|bc a2c 0   0   0   0   0   0   0   0   ad2 acd abd a2d 0   0   0  0   0   0  |
|                                                                             |
| b2c b2d bc2 bcd bd2 c3 c2d cd2 d3 |, {5} | a3 a2b a2c a2d ab2 abc abd ac2 ac|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|d-a2d2 ab3d-a3cd a2c2d-ab2d2 ac3d-abd3 b3c-ab2d b5-a2b2c ab2c2-b4d b2c3-b3d2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|      b2c2 b2c2 abc2 b3c  b3c  b2cd b2cd b2cd abcd 0       b2d2 bc3  b2d2 abd|
|2+b2d 0    0    0    -bc2 -bc2 0    0    0    0    bcd     0    0    0    0  |
|a2c   b2d  b2d  abd  -abc -abc bc2  bc2  bc2  ac2  b2c+abd bcd  bcd  bcd  acd|
|      -b3  -b3  -ab2 0    0    -abc -abc -abc -a2c -ab2    -abd -b2c -abd -a2|
|                                                                             |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -b3d -ab2d 0 0 0 -b2cd 0 0 0 0 0 0 0 |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b3c  ab2c  0 0 0 b2c2  0 0 0 0 0 0 0 |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b4   ab3   0 0 0 b3c   0 0 0 0 0 0 0 |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -ab3 -a2b2 0 0 0 -ab2c 0 0 0 0 0 0 0 |
|                                                                             |
| b2cd b2d2 bc3 bc2d bcd2 bd3 c4 c3d c2d2 cd3 d4 |, {5} | a4 a3b a3c a3d a2b2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|a3bd a2b4-a4bc a3bc2-a2b3d a2bc3-a2b2d2 a2bc2-a3cd a2b3c-a4c2 a3c3-a2b2cd a2c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| ab4   ab3d  ab3d  a2b2d 0          ab2c2 ab2c2 a2bc2 ab3c  ab3c  ab2cd ab2cd|
| -ab2c 0     0     0     -a2c2+ab2d 0     0     0     -abc2 -abc2 0     0    |
| -a2b2 ab2c  ab2c  a2bc  ab3-a3c    ab2d  ab2d  a2bd  -a2bc -a2bc abc2  abc2 |
| 0     -a2b2 -a2b2 -a3b  0          -ab3  -ab3  -a2b2 0     0     -a2bc -a2bc|
|                                                                             |
| -a2bcd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a2c2d -a2bcd -a3cd 0 0 0 0 0 0 0 0|
| a2bc2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a2c3   a2bc2  a3c2  0 0 0 0 0 0 0 0|
| a2b2c  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a2bc2  a2b2c  a3bc  0 0 0 0 0 0 0 0|
| -a3bc  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a3c2  -a3bc  -a4c  0 0 0 0 0 0 0 0|
|-----------------------------------------------------------------------------|
|2cd2 a2b2cd-a3bd2 a2b4d-a4bcd a3bc2d-a2b3d2 a2bc3d-a2b2d3 a2bc3-a3c2d a2b3c2-|
|                                                                             |
|                                                                             |
|bd3 -a2c2d2 -ab5 -a2b3c -ab4d -ab3c2 -ab4c -a2b2c2 -ab3cd -ab2c3 -ab4d -a2b2c|
|    0       ab3c ab3d   0     0      ab2c2 ab2cd   0      0      ab2cd ab2d2 |
|cd2 -a2d3   a2b3 ab4    -ab3c -ab3d  a2b2c ab3c    -ab2c2 -ab2cd a2b2d ab3d  |
|2   a2bd2   0    0      a2b3  ab4    0     0       a2b2c  ab3c   0     0     |
|                                                                             |
|b2d  a2bcd  a2bd2  a2c2d  a2cd2  a2d3   ab3d  ab2cd  ab2d2  abc2d  abcd2  abd|
|2b2c -a2bc2 -a2bcd -a2c3  -a2c2d -a2cd2 -ab3c -ab2c2 -ab2cd -abc3  -abc2d -ab|
|2b3  -a2b2c -a2b2d -a2bc2 -a2bcd -a2bd2 -ab4  -ab3c  -ab3d  -ab2c2 -ab2cd -ab|
|b2   a3bc   a3bd   a3c2   a3cd   a3d2   a2b3  a2b2c  a2b2d  a2bc2  a2bcd  a2b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |) <----------------------------------|
|0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |     {3} | 1 0 0 0 0 0  0 0 0 0  0 0 |
|0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |     {4} | 0 1 0 0 0 0  0 0 0 0  0 0 |
|bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |     {4} | 0 0 0 0 0 -1 0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  1 0 0 0  0 0 |
|                                             {3} | 0 0 1 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 1 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 -1 0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  1 0 |
|                                             {3} | 0 0 0 0 1 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 1 0 0  0 0 |
|                                             {3} | 0 0 0 0 0 0  0 0 1 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 1 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                                                             |
|  0  0  cd 0  0  0  d2 0  0  0  |, {4} | d  a2 0  0  0  ab 0  0  0  ac 0  0  |
|2 0  0  0  cd 0  0  0  d2 0  0  |  {4} | -c 0  a2 0  0  0  ab 0  0  0  ac 0  |
|  c2 0  0  0  cd 0  0  0  d2 0  |  {4} | -b 0  0  a2 0  0  0  ab 0  0  0  ac |
|  0  c2 0  0  0  cd 0  0  0  d2 |  {4} | a  0  0  0  a2 0  0  0  ab 0  0  0  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-abd2 b2c-abd b4-a2bc abc2-b3d bc3-b2d2 bc2-acd b3c-a2c2 ac3-b2cd c4-bcd2 bcd|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0|
|0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0|
|0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0|
|0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0  0   0   0   0  0   0   0   0  0   bcd bc2 b2c abc 0   0   0   0   0   0  |
| b3 ab2 0   0   0  0   0   0   0  0   0   0   0   0   bcd bc2 b2c abc 0   0  |
| 0  0   b2d b2c b3 ab2 0   0   0  0   0   0   0   0   0   0   0   0   bcd bc2|
| 0  0   0   0   0  0   b2d b2c b3 ab2 0   0   0   0   0   0   0   0   0   0  |
|                                                                             |
|d ad2 b3 b2c b2d bc2 bcd bd2 c3 c2d cd2 d3 |) <----- 0 : {-2, 5}             |
|                                                 0                           |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|b2c2-abcd b4c-a2bc2 abc3-b3cd bc4-b2cd2 b2cd-abd2 b4d-a2bcd abc2d-b3d2 bc3d-b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2 0       bc2d bc2d bc3  ac3  0       0        bc2d ac2d 0       bcd2 bcd2 c4|
|  bd2     0    0    0    0    c3      0        0    0    c2d     0    0    0 |
|  ac2+b2d bd2  bd2  bcd  acd  ac2+b2d c3-bd2   bd2  ad2  bc2+acd c2d  c2d  c2|
|d -a2c    -b2d -b2d -b2c -abc -b3     -ac2+b2d -b2d -abd -abc    -acd -acd -b|
|                                                                             |
|0 0 0 0 0 0 0 0 0 0 -bc2d -b2cd -abcd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 bc3   b2c2  abc2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 b2c2  b3c   ab2c  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 -abc2 -ab2c -a2bc 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                                                                             |
|a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|4-a2bcd2 a2bcd-a3d2 a2b3d-a4cd a3c2d-a2b2d2 a2c3d-a2bd3 ab3c-a2b2d ab5-a3b2c |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| ab2cd a2bcd 0         ab2d2 abc3  ab2d2 a2bd2 0         abc2d abc2d abc3  a2|
| 0     0     abcd      0     0     0     0     abd2      0     0     0     0 |
| abc2  a2c2  ab2c+a2bd abcd  abcd  abcd  a2cd  a2c2+ab2d abd2  abd2  abcd  a2|
| -a2bc -a3c  -a2b2     -a2bd -ab2c -a2bd -a3d  -a3c      -ab2d -ab2d -ab2c -a|
|                                                                             |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -ab3d -a2b2d 0 0 0 -ab2cd 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ab3c  a2b2c  0 0 0 ab2c2  0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ab4   a2b3   0 0 0 ab3c   0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a2b3 -a3b2  0 0 0 -a2b2c 0 0 0 0 0 0 0 0 0 |
|-----------------------------------------------------------------------------|
|a4c3 a3c4-a2b2c2d a2c5-a2bc2d2 a2bc2d-a3cd2 a2b3cd-a4c2d a3c3d-a2b2cd2 a2c4d-|
|                                                                             |
|                                                                             |
|d -ab3d2 -ab2c2d -ab3c2 -a2bc3 -ab2c2d -abc4  -ab3cd -a2bc2d -ab2cd2 -abc3d -|
|  0      0       abc3   abc2d  0       0      abc2d  abcd2   0       0      a|
|  -ab2cd -ab2d2  a2bc2  ab2c2  -abc3   -abc2d a2bcd  ab2cd   -abc2d  -abcd2 a|
|  a2b2d  ab3d    0      0      a2bc2   ab2c2  0      0       a2bcd   ab2cd  0|
|                                                                             |
|3   ac3d  ac2d2  acd3   ad4   b4d  b3cd  b3d2  b2c2d b2cd2  b2d3   bc3d  bc2d|
|cd2 -ac4  -ac3d  -ac2d2 -acd3 -b4c -b3c2 -b3cd -b2c3 -b2c2d -b2cd2 -bc4  -bc3|
|2d2 -abc3 -abc2d -abcd2 -abd3 -b5  -b4c  -b4d  -b3c2 -b3cd  -b3d2  -b2c3 -b2c|
|d2  a2c3  a2c2d  a2cd2  a2d3  ab4  ab3c  ab3d  ab2c2 ab2cd  ab2d2  abc3  abc2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|--- cokernel {3} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
||            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 |
||            {3} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
||            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 |
||            {3} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
||            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 |
||            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d |
||            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
||            {3} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 |
||            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
||            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
||            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
|                                                                             |
|0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2|
|0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0 |
|0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0 |
|ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-ad2 b3d-a2cd ac2d-b2d2 c3d-bd3 a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3 b2c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0 |
|   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0 |
|   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0 |
|d2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bc|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   c2d |
| 0   0   0   0   0   0   bd2 bcd b2d abd 0   0   0   0   0   0   0   0   0   |
| b2c abc 0   0   0   0   0   0   0   0   bd2 bcd b2d abd 0   0   0   0   0   |
| 0   0   bcd bc2 b2c abc 0   0   0   0   0   0   0   0   bd2 bcd b2d abd 0   |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2d3 bc3-ac2d b3c2-a2c3 ac4-b2c2d c5-bc2d2 bc2d-acd2 b3cd-a2c2d ac3d-b2cd2 c4d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|   bcd2 0       bd3  c3d  c3d  0 bd3  0 acd2 acd2 acd2 c2d2 c2d2 0 0 0       |
|   0    cd2     0    0    0    0 0    0 -d3  -d3  -d3  0    0    0 0 -a2cd   |
|d  c2d  bcd+ad2 cd2  cd2  cd2  0 cd2  0 -bd2 -bd2 -bd2 d3   d3   0 0 -a2bc-a3|
|c2 -acd -abd    -ad2 -bcd -bcd 0 -ad2 0 0    0    0    -bd2 -bd2 0 0 a3b     |
|                                                                             |
| 0 0 0 0 -c3d -bc2d -ac2d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
| 0 0 0 0 c4   bc3   ac3   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
| 0 0 0 0 bc3  b2c2  abc2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
| 0 0 0 0 -ac3 -abc2 -a2c2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                                                                             |
|c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 bd3 c4 c3d c2d2 cd3 d4 |) <----- 0 : {-3, |
|                                                                0            |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|a2b2c2-ab4d ab2c3-ab3d2 ab2c2-a2bcd ab4c-a3bc2 a2bc3-ab3cd abc4-ab2cd2 ab2cd-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|c3  0         0          abc2d a2c2d 0         abcd2 abcd2 ac4   abcd2 0     |
|    ac3       0          0     0     ac2d      0     0     0     0     acd2  |
|cd  a2c2+ab2d ac3-abd2   abd2  a2d2  abc2+a2cd ac2d  ac2d  ac2d  ac2d  abcd+a|
|2bc -ab3      -a2c2+ab2d -ab2d -a2bd -a2bc     -a2cd -a2cd -abc2 -a2cd -a2bd |
|                                                                             |
|0 0 0 0 0 0 0 0 -abc2d -ab2cd -a2bcd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|0 0 0 0 0 0 0 0 abc3   ab2c2  a2bc2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|0 0 0 0 0 0 0 0 ab2c2  ab3c   a2b2c  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|0 0 0 0 0 0 0 0 -a2bc2 -a2b2c -a3bc  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|-----------------------------------------------------------------------------|
|a2bcd3 a2bcd2-a3d3 a2b3d2-a4cd2 a3c2d2-a2b2d3 a2c3d2-a2bd4 ab4c-a2b3d ab6-a3b|
|                                                                             |
|                                                                             |
|ab3d2 -a2bcd2 -ab2d3 -abc2d2 -ab2c3 -a2c4 -abc3d -ac5  -ab2c2d -a2c3d -abc2d2|
|bcd2  abd3    0      0       ac4    ac3d  0      0     ac3d    ac2d2  0      |
|2bd2  ab2d2   -abcd2 -abd3   a2c3   abc3  -ac4   -ac3d a2c2d   abc2d  -ac3d  |
|      0       a2bd2  ab2d2   0      0     a2c3   abc3  0       0      a2c2d  |
|                                                                             |
|2  bcd3   bd4   c4d  c3d2  c2d3   cd4   d5   0 0 0 0 |) <----- 0 : {-5, 7}   |
|d  -bc2d2 -bcd3 -c5  -c4d  -c3d2  -c2d3 -cd4 0 0 0 0 |     0                 |
|2d -b2cd2 -b2d3 -bc4 -bc3d -bc2d2 -bcd3 -bd4 0 0 0 0 |                       |
|d  abcd2  abd3  ac4  ac3d  ac2d2  acd3  ad4  0 0 0 0 |                       |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | : {-1, 2}                            |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 |                                      |
|0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 |                                      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a |                                      |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0  0  0  |) <----- 0 : {-1, 3}                                              |
| d2 0  0  |     0                                                            |
| 0  d2 0  |                                                                  |
| 0  0  d2 |                                                                  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| b2d bc2 bcd bd2 c3 c2d cd2 d3 |) <------------------------------- cokernel {|
|                                     {2} | 1 0 0 0 0 0 0 0 0 0 |            {|
|                                     {2} | 0 1 0 0 0 0 0 0 0 0 |            {|
|                                     {2} | 0 0 1 0 0 0 0 0 0 0 |            {|
|                                     {2} | 0 0 0 1 0 0 0 0 0 0 |            {|
|                                     {2} | 0 0 0 0 1 0 0 0 0 0 |            {|
|                                     {2} | 0 0 0 0 0 1 0 0 0 0 |            {|
|                                     {2} | 0 0 0 0 0 0 1 0 0 0 |            {|
|                                     {2} | 0 0 0 0 0 0 0 1 0 0 |            {|
|                                     {2} | 0 0 0 0 0 0 0 0 1 0 |            {|
|                                     {2} | 0 0 0 0 0 0 0 0 0 1 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {4} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {4} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {4} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {4} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {4} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {4} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {4} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {4} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {4} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {4} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {4} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {4} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                                                             |
|  bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0   0   d3 0  0  0  |, |
|  0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0   0   0  d3 0  0  |  |
|  0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2 0   0  0  d3 0  |  |
|d 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0   cd2 0  0  0  d3 |  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|c3 bc2 ac2 0   0  0   0   0   0  0   0   0   0  0   0   0   0   0   0   0   0|
|0  0   0   c2d c3 bc2 ac2 0   0  0   0   0   0  0   0   cd2 c2d bcd acd 0   0|
|0  0   0   0   0  0   0   c2d c3 bc2 ac2 0   0  0   0   0   0   0   0   cd2 c|
|0  0   0   0   0  0   0   0   0  0   0   c2d c3 bc2 ac2 0   0   0   0   0   0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-bcd3 bcd2-ad3 b3d2-a2cd2 ac2d2-b2d3 c3d2-bd4 a4 a3b a3c a3d a2b2 a2bc a2bd a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|  0         0 0 0 0 0 0 0 0 0 0 0 0 0 0          0 0          0          0 0 |
|  -a2cd     0 0 0 0 0 0 0 0 0 0 0 0 0 -a2c2+ab2d 0 -abcd      -abcd      0 0 |
|d -a2bc-a3d 0 0 0 0 0 0 0 0 0 0 0 0 0 ab3-a3c    0 -ab2c-a2bd -ab2c-a2bd 0 0 |
|  a3b       0 0 0 0 0 0 0 0 0 0 0 0 0 0          0 a2b2       a2b2       0 0 |
|                                                                             |
| 0 0 0 0 0 a2d  abd  acd  ad2  b2d  bcd  bd2  c2d  cd2  d3   a4 0  0  0  a3b |
| 0 0 0 0 0 -a2c -abc -ac2 -acd -b2c -bc2 -bcd -c3  -c2d -cd2 0  a4 0  0  0   |
| 0 0 0 0 0 -a2b -ab2 -abc -abd -b3  -b2c -b2d -bc2 -bcd -bd2 0  0  a4 0  0   |
| 0 0 0 0 0 a3   a2b  a2c  a2d  ab2  abc  abd  ac2  acd  ad2  0  0  0  a4 0   |
|                                                                             |
|6}                                                                           |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|a2bd2 ab4d-a3bcd a2bc2d-ab3d2 abc3d-ab2d3 abc3-a2c2d ab3c2-a3c3 a2c4-ab2c2d a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|    abd3  ac3d  ac3d  abd3  0 a2cd2 a2cd2 a2cd2 ac2d2 ac2d2 ab4   ab3c  b5   |
|    0     0     0     0     0 -ad3  -ad3  -ad3  0     0     -ab2c -abc2 -b3c |
|2d2 acd2  acd2  acd2  acd2  0 -abd2 -abd2 -abd2 ad3   ad3   -a2b2 -a2bc -ab3 |
|    -a2d2 -abcd -abcd -a2d2 0 0     0     0     -abd2 -abd2 0     0     0    |
|                                                                             |
|0 0 0 0 -ac3d -abc2d -a2c2d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 ac4   abc3   a2c3   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 abc3  ab2c2  a2bc2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 -a2c3 -a2bc2 -a3c2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|-----------------------------------------------------------------------------|
|3c a2b3c2-ab5d ab3c3-ab4d2 ab3c2-a2b2cd ab5c-a3b2c2 a2b2c3-ab4cd ab2c4-ab3cd2|
|                                                                             |
|                                                                             |
| -ac4d  -ab2cd2 -a2c2d2 -abcd3 -ac3d2 -ab2d3 -a2cd3 -abd4 -ac2d3 -b6 -ab4c -b|
| 0      ac2d2   acd3    0      0      acd3   ad4    0     0      b4c b4d   0 |
| -ac2d2 a2cd2   abcd2   -ac2d2 -acd3  a2d3   abd3   -acd3 -ad4   ab4 b5    -b|
| abc2d  0       0       a2cd2  abcd2  0      0      a2d3  abd3   0   0     ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|2} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|2} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|2} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 |
|2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 |
|2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 |
|2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a |
|2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|{2} | -ab2 -a2c -abd -ac2 -b3 -abc -b2d -bc2 -b2c -ac2 -bcd -c3 -b2d -acd -bd|
|{3} | ac   ad   0    0    bc  bd   0    0    c2   cd   0    0   cd   d2   0  |
|{3} | a2   ab   -ac  -ad  ab  b2   -bc  -bd  ac   bc   -c2  -cd ad   bd   -cd|
|{3} | 0    0    a2   ab   0   0    ab   b2   0    0    ac   bc  0    0    ad |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|   0   0   0   0   0   0   0  0   0   0   0  0   0   0   0  0   0   0   ad  b|
|   0   0   0   0   0   0   d3 cd2 bd2 ad2 0  0   0   0   0  0   0   0   -ac -|
|2d bcd acd 0   0   0   0   0  0   0   0   d3 cd2 bd2 ad2 0  0   0   0   -ab -|
|   0   0   cd2 c2d bcd acd 0  0   0   0   0  0   0   0   d3 cd2 bd2 ad2 a2  a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2c2 a2cd a2d2 ab3 ab2c ab2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0 0 0 0 0         0 0 0 0 0 0 0 0 0 0         0          0         0         |
|0 0 0 0 -ac3+abd2 0 0 0 0 0 0 0 0 0 -abc2+b3d -a2c2+ab2d -ac3+abd2 -ac3+b2cd+|
|0 0 0 0 0         0 0 0 0 0 0 0 0 0 b4-a2bc   ab3-a3c    0         b3c+ab2d  |
|0 0 0 0 ab3-a3c   0 0 0 0 0 0 0 0 0 0         0          ab3-a3c   -a3c      |
|                                                                             |
|0   0   0   a3c 0   0   0   a3d 0   0   0   a2b2 0    0    0    a2bc 0    0  |
|a3b 0   0   0   a3c 0   0   0   a3d 0   0   0    a2b2 0    0    0    a2bc 0  |
|0   a3b 0   0   0   a3c 0   0   0   a3d 0   0    0    a2b2 0    0    0    a2b|
|0   0   a3b 0   0   0   a3c 0   0   0   a3d 0    0    0    a2b2 0    0    0  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|c5-abc2d2 abc2d-a2cd2 ab3cd-a3c2d a2c3d-ab2cd2 ac4d-abcd3 abcd2-a2d3 ab3d2-a3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|b4d  b4d  ab3d  0         b3c2 b3c2 ab2c2 b4c   b4c   b3cd  b3cd  b3cd  ab2cd|
|0    0    0     -abc2+b3d 0    0    0     -b2c2 -b2c2 0     0     0     0    |
|b3c  b3c  ab2c  b4-a2bc   b3d  b3d  ab2d  -ab2c -ab2c b2c2  b2c2  b2c2  abc2 |
|-ab3 -ab3 -a2b2 0         -b4  -b4  -ab3  0     0     -ab2c -ab2c -ab2c -a2bc|
|                                                                             |
| 0 0 0 0 0 0 0 0 -b4d -ab3d 0 0 0 -b3cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -b2|
| 0 0 0 0 0 0 0 0 b4c  ab3c  0 0 0 b3c2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b2c|
| 0 0 0 0 0 0 0 0 b5   ab4   0 0 0 b4c   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b3c|
| 0 0 0 0 0 0 0 0 -ab4 -a2b3 0 0 0 -ab3c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -ab|
|-----------------------------------------------------------------------------|
| ab3cd-a2b2d2 ab5d-a3b2cd a2b2c2d-ab4d2 ab2c3d-ab3d3 ab2c3-a2bc2d ab4c2-a3bc3|
|                                                                             |
|                                                                             |
|5d -b4c2 -b5c -ab3c2 -b4cd -b3c3 -b5d -ab3cd -b4d2 -b3c2d -b4c2 -ab2c3 -b3c2d|
|   0     b3c2 b3cd   0     0     b3cd b3d2   0     0      b2c3  b2c2d  0     |
|4c -b4d  ab3c b4c    -b3c2 -b3cd ab3d b4d    -b3cd -b3d2  ab2c2 b3c2   -b2c3 |
|4  b5    0    0      ab3c  b4c   0    0      ab3d  b4d    0     0      ab2c2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0 0 0 0 | : {-2, 2}                                                          |
|0 0 0 0 |                                                                    |
|0 0 0 0 |                                                                    |
|0 0 0 0 |                                                                    |
|0 0 0 0 |                                                                    |
|0 0 0 0 |                                                                    |
|0 0 0 0 |                                                                    |
|0 0 0 0 |                                                                    |
|0 0 0 0 |                                                                    |
|d c b a |                                                                    |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2 -c2d a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0 |
|  0    0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0 |
|  -d2  0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab|
|  bd   0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|d  cd  d2  a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0 |
|bc -c2 -cd 0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab|
|b2 -bc -bd 0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0 |
|b  ac  ad  0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|b2cd b2d2 bc3 bc2d bcd2 bd3 c4 c3d c2d2 cd3 d4 |, | a2bc-a3d a2b3-a4c a3c2-a2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|     0 0 0 0 0 0         0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a2b2 -a3c -a2bd -a2c2 -|
|abd2 0 0 0 0 0 -bc3+ac2d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a2c   a2d  0     0     a|
|     0 0 0 0 0 -b3d+a2cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a3    a2b  -a2c  -a2d  a|
|     0 0 0 0 0 b4-a2bc   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0     0    a3    a2b   0|
|                                                                             |
|  0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    |
|  0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 |
|c 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    |
|  a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|cd2 a2c2d2-ab2d3 ac3d2-abd4 b4c-ab3d b6-a2b3c ab3c2-b5d b3c3-b4d2 b3c2-ab2cd |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0        b3d2  b2c3 b3d2  ab2d2 0        b2c2d b2c2d b2c3 abc3  0        0  |
| b2cd     0     0    0     0     b2d2     0     0     0    0     bc3      0  |
| b3c+ab2d b2cd  b2cd b2cd  abcd  abc2+b3d b2d2  b2d2  b2cd abcd  abc2+b3d bc3|
| -ab3     -ab2d -b3c -ab2d -a2bd -a2bc    -b3d  -b3d  -b3c -ab2c -b4      -ab|
|                                                                             |
|c2d -b3cd -ab2cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -bc3d -b2c2d|
|3   b3c2  ab2c2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 bc4   b2c3  |
|2   b4c   ab3c   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b2c3  b3c2  |
|2c2 -ab3c -a2b2c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -abc3 -ab2c2|
|-----------------------------------------------------------------------------|
| a2bc4-ab3c2d abc5-ab2c2d2 ab2c2d-a2bcd2 ab4cd-a3bc2d a2bc3d-ab3cd2 abc4d-ab2|
|                                                                             |
|                                                                             |
| -b2c4  -b4cd -ab2c2d -b3cd2 -b2c3d -b4d2 -ab2cd2 -b3d3  -b2c2d2 -b3c3 -abc4 |
| 0      b2c2d b2cd2   0      0      b2cd2 b2d3    0      0       bc4   bc3d  |
| -b2c2d ab2cd b3cd    -b2c2d -b2cd2 ab2d2 b3d2    -b2cd2 -b2d3   abc3  b2c3  |
| b3c2   0     0       ab2cd  b3cd   0     0       ab2d2  b3d2    0     0     |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|  0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0  |
|  0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2|
|2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0  |
|  ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|  0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2|
|2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0  |
|  ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0  |
|  0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|b2d a2c3-a2bd2 ab2c-a2bd ab4-a3bc a2bc2-ab3d abc3-ab2d2 abc2-a2cd ab3c-a3c2 a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|ab3 -a2bc -ab2d -abc2 -ab2c -a2c2 -abcd -ac3 -ab2d -a2cd -abd2 -ac2d -b4 -ab2|
|bc  abd   0     0     ac2   acd   0     0    acd   ad2   0     0     b2c b2d |
|2b  ab2   -abc  -abd  a2c   abc   -ac2  -acd a2d   abd   -acd  -ad2  ab2 b3  |
|    0     a2b   ab2   0     0     a2c   abc  0     0     a2d   abd   0   0   |
|                                                                             |
|0    0    ab3 0   0   0   ab2c 0    0    0    ab2d 0    0    0    abc2 0    0|
|0    0    0   ab3 0   0   0    ab2c 0    0    0    ab2d 0    0    0    abc2 0|
|a2d2 0    0   0   ab3 0   0    0    ab2c 0    0    0    ab2d 0    0    0    a|
|0    a2d2 0   0   0   ab3 0    0    0    ab2c 0    0    0    ab2d 0    0    0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|b5c-a2b2c2 ab2c3-b4cd b2c4-b3cd2 b3cd-ab2d2 b5d-a2b2cd ab2c2d-b4d2 b2c3d-b3d3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|       b2c2d abc2d 0         b2cd2 b2cd2 bc4   b2cd2 abcd2 0         b2d3  bc|
|       0     0     bc2d      0     0     0     0     0     bcd2      0     0 |
|-b2d2  b2d2  abd2  b2c2+abcd bc2d  bc2d  bc2d  bc2d  ac2d  b2cd+abd2 bcd2  bc|
|c2+b3d -b3d  -ab2d -ab2c     -abcd -abcd -b2c2 -abcd -a2cd -ab2d     -abd2 -b|
|                                                                             |
| -abc2d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -c4|
| abc3   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c5 |
| ab2c2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 bc4|
| -a2bc2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -ac|
|-----------------------------------------------------------------------------|
|cd3 ab2cd2-a2bd3 ab4d2-a3bcd2 a2bc2d2-ab3d3 abc3d2-ab2d4 abc4-a2c3d ab3c3-a3c|
|                                                                             |
|                                                                             |
|-b2c3d -bc5  -b3c2d -abc3d -b2c2d2 -bc4d  -b3cd2 -abc2d2 -b2cd3 -bc3d2 -b3d3 |
|0      0     bc3d   bc2d2  0       0      bc2d2  bcd3    0      0      bcd3  |
|-bc4   -bc3d abc2d  b2c2d  -bc3d   -bc2d2 abcd2  b2cd2   -bc2d2 -bcd3  abd3  |
|abc3   b2c3  0      0      abc2d   b2c2d  0      0       abcd2  b2cd2  0     |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   |
| 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd |
| ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   |
| 0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd |
| ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   |
| 0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   |
| 0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2c3-ab2cd ac4-abcd2 abcd-a2d2 ab3d-a3cd a2c2d-ab2d2 ac3d-abd3 b3c-ab2d b5-a2b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|c -b3d -b2c2 -b3c -abc2 -b2cd -bc3 -b3d -abcd -b2d2 -bc2d -b2c2 -ac3 -bc2d -c|
|  0    0     bc2  bcd   0     0    bcd  bd2   0     0     c3    c2d  0     0 |
|  -b2c -b2d  abc  b2c   -bc2  -bcd abd  b2d   -bcd  -bd2  ac2   bc2  -c3   -c|
|  ab2  b3    0    0     abc   b2c  0    0     abd   b2d   0     0    ac2   bc|
|                                                                             |
|    0    abcd 0    0    0    abd2 0    0    0    ac3 0   0   0   ac2d 0    0 |
|    0    0    abcd 0    0    0    abd2 0    0    0   ac3 0   0   0    ac2d 0 |
|bc2 0    0    0    abcd 0    0    0    abd2 0    0   0   ac3 0   0    0    ac|
|    abc2 0    0    0    abcd 0    0    0    abd2 0   0   0   ac3 0    0    0 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| b2c3-abc2d b4c2-a2bc3 abc4-b3c2d bc5-b2c2d2 b2c2d-abcd2 b4cd-a2bc2d abc3d-b3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|3d  bc3d  b2d3  abd3  0         bc2d2 bc2d2 c5             bc4   ac4   0     |
|    0     0     0     bd3       0     0     0              0     0     c4    |
|d2  bcd2  bcd2  acd2  ac2d+b2d2 bd3   bd3   bd3            bc2d  ac2d  b2cd+a|
|2cd -b2cd -abd2 -a2d2 -a2cd     -b2d2 -b2d2 -bc3+ac2d-b2d2 -b2c2 -abc2 -b3c+a|
|                                                                             |
|d -bc3d -ac3d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|  bc4   ac4   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|  b2c3  abc3  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|4 -abc3 -a2c3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|-----------------------------------------------------------------------------|
|4 a2c5-ab2c3d ac6-abc3d2 abc3d-a2c2d2 ab3c2d-a3c3d a2c4d-ab2c2d2 ac5d-abc2d3 |
|                                                                             |
|                                                                             |
|-abcd3 -b2d4 -bc2d3 -b2c4 -ac5 -bc4d -c6  -b2c3d -ac4d -bc3d2 -c5d  -b2c2d2 -|
|bd4    0     0      c5    c4d  0     0    c4d    c3d2  0      0     c3d2    c|
|b2d3   -bcd3 -bd4   ac4   bc4  -c5   -c4d ac3d   bc3d  -c4d   -c3d2 ac2d2   b|
|0      abd3  b2d3   0     0    ac4   bc4  0      0     ac3d   bc3d  0       0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0   0   d3 0  0  |
|0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0   0   0  d3 0  |
|bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2 0   0  0  d3 |
|0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0   cd2 0  0  0  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0   0   d3 0 |
|bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0   0   0  d3|
|0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2 0   0  0 |
|0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0   cd2 0  0 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2c ab2c2-b4d b2c3-b3d2 b2c2-abcd b4c-a2bc2 abc3-b3cd bc4-b2cd2 b2cd-abd2 b4d-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|4  -b2cd -ac2d -bcd2 -c3d -b2d2 -acd2 -bd3 -c2d2 a4 0  0  0  a3b 0   0   0   |
|   c2d   cd2   0     0    cd2   d3    0    0     0  a4 0  0  0   a3b 0   0   |
|2d acd   bcd   -c2d  -cd2 ad2   bd2   -cd2 -d3   0  0  a4 0  0   0   a3b 0   |
|2  0     0     acd   bcd  0     0     ad2  bd2   0  0  0  a4 0   0   0   a3b |
|                                                                             |
|   0    acd2 0    0    0    ad3 0   0   0   b4 0  0  0  b3c 0   0   0   b3d 0|
|   0    0    acd2 0    0    0   ad3 0   0   0  b4 0  0  0   b3c 0   0   0   b|
|2d 0    0    0    acd2 0    0   0   ad3 0   0  0  b4 0  0   0   b3c 0   0   0|
|   ac2d 0    0    0    acd2 0   0   0   ad3 0  0  0  b4 0   0   0   b3c 0   0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|cd2 bc4d-b2cd3 b2cd2-abd3 b4d2-a2bcd2 abc2d2-b3d3 bc3d2-b2d4 bc4-ac3d b3c3-a2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|         0         bc3d  ac3d  0         0          bc2d2 ac2d2 0         bcd|
|         0         0     0     c3d       0          0     0     c2d2      0  |
|bd2      c4-bcd2   bcd2  acd2  ac2d+b2d2 c3d-bd3    bd3   ad3   bc2d+acd2 c2d|
|2c2-ab2d -ac3+b2cd -b2cd -abcd -b3d      -ac2d+b2d2 -b2d2 -abd2 -abcd     -ac|
|                                                                             |
| 0 0 0 0 0 0 0 0 a3d  a2bd  a2cd  a2d2  ab2d  abcd  abd2  ac2d  acd2  ad3   b|
| 0 0 0 0 0 0 0 0 -a3c -a2bc -a2c2 -a2cd -ab2c -abc2 -abcd -ac3  -ac2d -acd2 -|
| 0 0 0 0 0 0 0 0 -a3b -a2b2 -a2bc -a2bd -ab3  -ab2c -ab2d -abc2 -abcd -abd2 -|
| 0 0 0 0 0 0 0 0 a4   a3b   a3c   a3d   a2b2  a2bc  a2bd  a2c2  a2cd  a2d2  a|
|-----------------------------------------------------------------------------|
|abc2d2-a2cd3 ab3cd2-a3c2d2 a2c3d2-ab2cd3 ac4d2-abcd4 abcd3-a2d4 ab3d3-a3cd3 a|
|                                                                             |
|                                                                             |
|ac3d2 -bc2d3 -c4d2 -b2cd3 -ac2d3 -bcd4 -c3d3 -b2d4 -acd4 -bd5 -c2d4 0 0 0 0 ||
|2d3   0      0     c2d3   cd4    0     0     cd4   d5    0    0     0 0 0 0 ||
|c2d2  -c3d2  -c2d3 acd3   bcd3   -c2d3 -cd4  ad4   bd4   -cd4 -d5   0 0 0 0 ||
|      ac2d2  bc2d2 0      0      acd3  bcd3  0     0     ad4  bd4   0 0 0 0 ||
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0  |) <------------------------------------------------------------------- co|
|0  |     {4} | 1 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|0  |     {5} | 0 1 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|d3 |     {5} | 0 0 0 0 0 -1 0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 -1 0 0 0 0  0 0 0 0  0 0 |     |
|         {4} | 0 0 1 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 1 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 -1 0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 -1 0 0 0 0  0 0 |     |
|         {4} | 0 0 0 0 1 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  1 0 0 0  0 0 0 0  0 0 |     |
|         {4} | 0 0 0 0 0 0  1 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  1 0 0 0  0 0 |     |
|         {4} | 0 0 0 0 0 0  0 1 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 1 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 -1 0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 -1 0 0 |     |
|         {4} | 0 0 0 0 0 0  0 0 0 1 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {4} | 0 0 0 0 0 0  0 0 0 0 0  1 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  1 0 |     |
|         {4} | 0 0 0 0 0 0  0 0 0 0 0  0 0  1 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 1 0 0  0 0 0 0  0 0 |     |
|         {4} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 1 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 1 0 0  0 0 |     |
|         {4} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 1 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 1 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|                                                                             |
| 0  0  |, {4} | ad  bd  cd  d2  a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a|
| 0  0  |  {4} | -ac -bc -c2 -cd 0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0|
| d3 0  |  {4} | -ab -b2 -bc -bd 0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0|
| 0  d3 |  {4} | a2  ab  ac  ad  0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|a2bcd abc2d-b3d2 bc3d-b2d3 bc3-ac2d b3c2-a2c3 ac4-b2c2d c5-bc2d2 bc2d-acd2 b3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|a3c 0   0   0   a3d 0   0   0   a2b2 0    0    0    a2bc 0    0    0    a2bd |
|0   a3c 0   0   0   a3d 0   0   0    a2b2 0    0    0    a2bc 0    0    0    |
|0   0   a3c 0   0   0   a3d 0   0    0    a2b2 0    0    0    a2bc 0    0    |
|0   0   0   a3c 0   0   0   a3d 0    0    0    a2b2 0    0    0    a2bc 0    |
|                                                                             |
|   0   0   b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0    bc3 0 |
|3d 0   0   0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0   bc|
|   b3d 0   0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0   0 |
|   0   b3d 0    0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0   0 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|c4 ac5-b2c3d c6-bc3d2 bc3d-ac2d2 b3c2d-a2c3d ac4d-b2c2d2 c5d-bc2d3 bc2d2-acd3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|3  bcd3  c4d   c4d   bcd3  0        bd4  c3d2  c3d2  0 bd4  0 acd3 acd3 acd3 |
|   0     0     0     0     cd3      0    0     0     0 0    0 -d4  -d4  -d4  |
|2  c2d2  c2d2  c2d2  c2d2  bcd2+ad3 cd3  cd3   cd3   0 cd3  0 -bd3 -bd3 -bd3 |
|d2 -acd2 -bc2d -bc2d -acd2 -abd2    -ad3 -bcd2 -bcd2 0 -ad3 0 0    0    0    |
|                                                                             |
|3d  b2cd  b2d2  bc2d  bcd2  bd3   c3d  c2d2  cd3   d4   0 0 0 0 |, {4} | a3d |
|b3c -b2c2 -b2cd -bc3  -bc2d -bcd2 -c4  -c3d  -c2d2 -cd3 0 0 0 0 |  {4} | -a3c|
|b4  -b3c  -b3d  -b2c2 -b2cd -b2d2 -bc3 -bc2d -bcd2 -bd3 0 0 0 0 |  {4} | -a3b|
|b3  ab2c  ab2d  abc2  abcd  abd2  ac3  ac2d  acd2  ad3  0 0 0 0 |  {4} | a4  |
|-----------------------------------------------------------------------------|
|2c2d3-ab2d4 ac3d3-abd5 b5c-ab4d b7-a2b4c ab4c2-b6d b4c3-b5d2 b4c2-ab3cd b6c-a|
|                                                                             |
|                                                                             |
|, {2} | -a4b2 -a5c -a4bd -a4c2 -a3b3 -a4bc -a3b2d -a3bc2 -a3b2c -a4c2 -a3bcd |
|  {3} | a4c   a4d  0     0     a3bc  a3bd  0      0      a3c2   a3cd  0      |
|  {3} | a5    a4b  -a4c  -a4d  a4b   a3b2  -a3bc  -a3bd  a4c    a3bc  -a3c2  |
|  {3} | 0     0    a5    a4b   0     0     a4b    a3b2   0      0     a4c    |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|kernel {4} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {4} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {4} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {4} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0 |
|   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0 |
|   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0 |
|   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|cd-a2c2d ac3d-b2cd2 c4d-bcd3 bcd2-ad3 b3d2-a2cd2 ac2d2-b2d3 c3d2-bd4 a4 a3b a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0    0    ab|
|a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0    0 |
|0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0 |
|0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0 |
|                                                                             |
|  0   0   bc2d 0    0    0    bcd2 0    0    0    bd3 0   0   0   c4 0  0  0 |
|3 0   0   0    bc2d 0    0    0    bcd2 0    0    0   bd3 0   0   0  c4 0  0 |
|  bc3 0   0    0    bc2d 0    0    0    bcd2 0    0   0   bd3 0   0  0  c4 0 |
|  0   bc3 0    0    0    bc2d 0    0    0    bcd2 0   0   0   bd3 0  0  0  c4|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| b3cd2-a2c2d2 ac3d2-b2cd3 c4d2-bcd4 bcd3-ad4 b3d3-a2cd3 ac2d3-b2d4 c3d3-bd5 0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|c2d3 c2d3 0 0 0         0         0 0 0 0 0 0 0 0 0 0 0 0 0 0           0 0  |
|0    0    0 0 -a3cd     -a3cd     0 0 0 0 0 0 0 0 0 0 0 0 0 -a3c2+a2b2d 0 -a2|
|d4   d4   0 0 -a3bc-a4d -a3bc-a4d 0 0 0 0 0 0 0 0 0 0 0 0 0 a2b3-a4c    0 -a2|
|-bd3 -bd3 0 0 a4b       a4b       0 0 0 0 0 0 0 0 0 0 0 0 0 0           0 a3b|
|                                                                             |
| a2bd  a2cd  a2d2  ab2d  abcd  abd2  ac2d  acd2  ad3   b3d  b2cd  b2d2  bc2d |
| -a2bc -a2c2 -a2cd -ab2c -abc2 -abcd -ac3  -ac2d -acd2 -b3c -b2c2 -b2cd -bc3 |
| -a2b2 -a2bc -a2bd -ab3  -ab2c -ab2d -abc2 -abcd -abd2 -b4  -b3c  -b3d  -b2c2|
| a3b   a3c   a3d   a2b2  a2bc  a2bd  a2c2  a2cd  a2d2  ab3  ab2c  ab2d  abc2 |
|-----------------------------------------------------------------------------|
|2b3c2 ab3c3-b5cd b3c4-b4cd2 b4cd-ab3d2 b6d-a2b3cd ab3c2d-b5d2 b3c3d-b4d3 b3c3|
|                                                                             |
|                                                                             |
|-a3c3 -a3b2d -a4cd -a3bd2 -a3c2d -a2b4 -a3b2c -a2b3d -a2b2c2 -a2b3c -a3bc2 -a|
|0     a3cd   a3d2  0      0      a2b2c a2b2d  0      0       a2bc2  a2bcd  0 |
|-a3cd a4d    a3bd  -a3cd  -a3d2  a3b2  a2b3   -a2b2c -a2b2d  a3bc   a2b2c  -a|
|a3bc  0      0     a4d    a3bd   0     0      a3b2   a2b3    0      0      a3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|  acd 0   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0  |
|  0   acd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0  |
|  0   0   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0  |
|2 0   0   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab2d abc2 abcd abd2 ac3 ac2d ac|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|3 0   0   0   ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abc|
|  ab3 0   0   0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0  |
|  0   ab3 0   0    0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0  |
|  0   0   ab3 0    0    0    ab2c 0    0    0    ab2d 0    0    0    abc2 0  |
|                                                                             |
| c3d 0   0   0   c2d2 0    0    0    cd3 0   0   0   d4 0  0  0  |, {4} | a2d|
| 0   c3d 0   0   0    c2d2 0    0    0   cd3 0   0   0  d4 0  0  |  {4} | -a2|
| 0   0   c3d 0   0    0    c2d2 0    0   0   cd3 0   0  0  d4 0  |  {4} | -a2|
| 0   0   0   c3d 0    0    0    c2d2 0   0   0   cd3 0  0  0  d4 |  {4} | a3 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| |, | a3bc-a4d a3b3-a5c a4c2-a3b2d a3c3-a3bd2 a2b2c-a3bd a2b4-a4bc a3bc2-a2b3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|         0           0 0 0 0 0 0 0           0 0 0 0 0 0 0 0 0 0           0 |
|bcd      -a2bcd      0 0 0 0 0 0 -a2c3+a2bd2 0 0 0 0 0 0 0 0 0 -a2bc2+ab3d -a|
|b2c-a3bd -a2b2c-a3bd 0 0 0 0 0 0 0           0 0 0 0 0 0 0 0 0 ab4-a3bc    a2|
|2        a3b2        0 0 0 0 0 0 a2b3-a4c    0 0 0 0 0 0 0 0 0 0           0 |
|                                                                             |
| bcd2  bd3   c3d  c2d2  cd3   d4   0 0 0 0 |) <----- 0 : {-4, 6}             |
| -bc2d -bcd2 -c4  -c3d  -c2d2 -cd3 0 0 0 0 |     0                           |
| -b2cd -b2d2 -bc3 -bc2d -bcd2 -bd3 0 0 0 0 |                                 |
| abcd  abd2  ac3  ac2d  acd2  ad3  0 0 0 0 |                                 |
|-----------------------------------------------------------------------------|
|-ab2c2d b5c2-a2b2c3 ab2c4-b4c2d b2c5-b3c2d2 b3c2d-ab2cd2 b5cd-a2b2c2d ab2c3d-|
|                                                                             |
|                                                                             |
|2b2cd -a2bc3 -a2b3d -a3bcd -a2b2d2 -a2bc2d -a2b2c2 -a3c3 -a2bc2d -a2c4  -a2b2|
|      0      a2bcd  a2bd2  0       0       a2c3    a2c2d 0       0      a2c2d|
|2bc2  -a2bcd a3bd   a2b2d  -a2bcd  -a2bd2  a3c2    a2bc2 -a2c3   -a2c2d a3cd |
|bc    a2b2c  0      0      a3bd    a2b2d   0       0     a3c2    a2bc2  0    |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | : {-2, 3}       |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a |                 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| bc2 0   0   0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   |
| 0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   |
| 0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   |
| 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|d2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 bd3 c4 c3d c2d2 cd3 d4 |) <---|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                             |
|d 0    0    0    abd2 0    0    0    ac3 0   0   0   ac2d 0    0    0    acd2|
|  abcd 0    0    0    abd2 0    0    0   ac3 0   0   0    ac2d 0    0    0   |
|  0    abcd 0    0    0    abd2 0    0   0   ac3 0   0    0    ac2d 0    0   |
|  0    0    abcd 0    0    0    abd2 0   0   0   ac3 0    0    0    ac2d 0   |
|                                                                             |
|  abd  acd  ad2  b2d  bcd  bd2  c2d  cd2  d3   a4 0  0  0  a3b 0   0   0   a3|
|c -abc -ac2 -acd -b2c -bc2 -bcd -c3  -c2d -cd2 0  a4 0  0  0   a3b 0   0   0 |
|b -ab2 -abc -abd -b3  -b2c -b2d -bc2 -bcd -bd2 0  0  a4 0  0   0   a3b 0   0 |
|  a2b  a2c  a2d  ab2  abc  abd  ac2  acd  ad2  0  0  0  a4 0   0   0   a3b 0 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|d a2bc3-a2b2d2 a2bc2-a3cd a2b3c-a4c2 a3c3-a2b2cd a2c4-a2bcd2 a2bcd-a3d2 a2b3d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|          0           0                 0 0 0 0 0 0           0 0 0 0 0 0 0 0|
|3c2+a2b2d -a2c3+a2bd2 -a2c3+ab2cd+a2bd2 0 0 0 0 0 -abc3+a2c2d 0 0 0 0 0 0 0 0|
|b3-a4c    0           ab3c+a2b2d        0 0 0 0 0 -ab3d+a3cd  0 0 0 0 0 0 0 0|
|          a2b3-a4c    -a4c              0 0 0 0 0 ab4-a3bc    0 0 0 0 0 0 0 0|
|-----------------------------------------------------------------------------|
|b4cd2 b2c4d-b3cd3 b3cd2-ab2d3 b5d2-a2b2cd2 ab2c2d2-b4d3 b2c3d2-b3d4 b2c4-abc3|
|                                                                             |
|                                                                             |
|cd -a3c2d -a2bcd2 -a2c3d -a2b2d2 -a3cd2 -a2bd3 -a2c2d2 -ab5 -a2b3c -ab4d -ab3|
|   a2cd2  0       0      a2cd2   a2d3   0      0       ab3c ab3d   0     0   |
|   a2bcd  -a2c2d  -a2cd2 a3d2    a2bd2  -a2cd2 -a2d3   a2b3 ab4    -ab3c -ab3|
|   0      a3cd    a2bcd  0       0      a3d2   a2bd2   0    0      a2b3  ab4 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|cd2 0   0   0   d3 0  0  0  |) <----- 0 : {-2, 4}                            |
|0   cd2 0   0   0  d3 0  0  |     0                                          |
|0   0   cd2 0   0  0  d3 0  |                                                |
|0   0   0   cd2 0  0  0  d3 |                                                |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|------------------------------------------------ cokernel {3} | d c b a 0 0 0|
|3} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 d c b|
|3} | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|                                                                             |
| 0    0    0    ad3 0   0   0   b4 0  0  0  b3c 0   0   0   b3d 0   0   0   b|
| acd2 0    0    0   ad3 0   0   0  b4 0  0  0   b3c 0   0   0   b3d 0   0   0|
| 0    acd2 0    0   0   ad3 0   0  0  b4 0  0   0   b3c 0   0   0   b3d 0   0|
| 0    0    acd2 0   0   0   ad3 0  0  0  b4 0   0   0   b3c 0   0   0   b3d 0|
|                                                                             |
|c 0   0   0   a3d 0   0   0   a2b2 0    0    0    a2bc 0    0    0    a2bd 0 |
|  a3c 0   0   0   a3d 0   0   0    a2b2 0    0    0    a2bc 0    0    0    a2|
|  0   a3c 0   0   0   a3d 0   0    0    a2b2 0    0    0    a2bc 0    0    0 |
|  0   0   a3c 0   0   0   a3d 0    0    0    a2b2 0    0    0    a2bc 0    0 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-a4cd a3c2d-a2b2d2 a2c3d-a2bd3 ab3c-a2b2d ab5-a3b2c a2b2c2-ab4d ab2c3-ab3d2 a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0 0 0 0 0 0 0 0          0           0           0                0 0 0 0 0 |
| 0 0 0 0 0 0 0 -ab2c2+b4d -a2bc2+ab3d -abc3+a2c2d -abc3+b3cd+a2c2d 0 0 0 0 0 |
| 0 0 0 0 0 0 0 b5-a2b2c   ab4-a3bc    -ab3d+a3cd  b4c+a3cd         0 0 0 0 0 |
| 0 0 0 0 0 0 0 0          0           ab4-a3bc    -a3bc            0 0 0 0 0 |
|-----------------------------------------------------------------------------|
|d b4c3-a2bc4 abc5-b3c3d bc6-b2c3d2 b2c3d-abc2d2 b4c2d-a2bc3d abc4d-b3c2d2 bc5|
|                                                                             |
|                                                                             |
|c2 -ab4c -a2b2c2 -ab3cd -ab2c3 -ab4d -a2b2cd -ab3d2 -ab2c2d -ab3c2 -a2bc3 -ab|
|   ab2c2 ab2cd   0      0      ab2cd ab2d2   0      0       abc3   abc2d  0  |
|d  a2b2c ab3c    -ab2c2 -ab2cd a2b2d ab3d    -ab2cd -ab2d2  a2bc2  ab2c2  -ab|
|   0     0       a2b2c  ab3c   0     0       a2b2d  ab3d    0      0      a2b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0    bc3 0   0   0   bc|
|    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0   bc3 0   0   0 |
|    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0   0   bc3 0   0 |
|    0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0   0   0   bc3 0 |
|                                                                             |
|   0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0    0    ab3 |
|bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0    0   |
|   a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0   |
|   0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0   |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|b2c2-a2bcd ab4c-a3bc2 a2bc3-ab3cd abc4-ab2cd2 ab2cd-a2bd2 ab4d-a3bcd a2bc2d-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0           0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a3b2 -a4c -a3bd -a3c2 -a|
|-b2c3+abc2d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a3c   a3d  0     0     a2|
|-b4d+a2bcd  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a4    a3b  -a3c  -a3d  a3|
|b5-a2b2c    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0     0    a4    a3b   0 |
|-----------------------------------------------------------------------------|
|d-b2c2d3 b2c2d2-abcd3 b4cd2-a2bc2d2 abc3d2-b3cd3 bc4d2-b2cd4 b2cd3-abd4 b4d3-|
|                                                                             |
|                                                                             |
|2c2d -abc4  -ab3cd -a2bc2d -ab2cd2 -abc3d -ab3d2 -a2bcd2 -ab2d3 -abc2d2 -ab2c|
|     0      abc2d  abcd2   0       0      abcd2  abd3    0      0       ac4  |
|c3   -abc2d a2bcd  ab2cd   -abc2d  -abcd2 a2bd2  ab2d2   -abcd2 -abd3   a2c3 |
|c2   ab2c2  0      0       a2bcd   ab2cd  0      0       a2bd2  ab2d2   0    |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | : {-3|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a |      |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2d 0    0    0    bcd2 0    0    0    bd3 0   0   0   c4 0  0  0  c3d 0   0  |
|   bc2d 0    0    0    bcd2 0    0    0   bd3 0   0   0  c4 0  0  0   c3d 0  |
|   0    bc2d 0    0    0    bcd2 0    0   0   bd3 0   0  0  c4 0  0   0   c3d|
|   0    0    bc2d 0    0    0    bcd2 0   0   0   bd3 0  0  0  c4 0   0   0  |
|                                                                             |
|0   0   0   ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd |
|ab3 0   0   0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    |
|0   ab3 0   0    0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    |
|0   0   ab3 0    0    0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|b3d2 abc3d-ab2d3 abc3-a2c2d ab3c2-a3c3 a2c4-ab2c2d ac5-abc2d2 abc2d-a2cd2 ab3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2b3 -a3bc -a2b2d -a2bc2 -a2b2c -a3c2 -a2bcd -a2c3 -a2b2d -a3cd -a2bd2 -a2c2d |
|bc  a2bd  0      0      a2c2   a2cd  0      0     a2cd   a2d2  0      0      |
|b   a2b2  -a2bc  -a2bd  a3c    a2bc  -a2c2  -a2cd a3d    a2bd  -a2cd  -a2d2  |
|    0     a3b    a2b2   0      0     a3c    a2bc  0      0     a3d    a2bd   |
|-----------------------------------------------------------------------------|
|a2bcd3 abc2d3-b3d4 bc3d3-b2d5 bc5-ac4d b3c4-a2c5 ac6-b2c4d c7-bc4d2 bc4d-ac3d|
|                                                                             |
|                                                                             |
|3 -a2c4 -abc3d -ac5  -ab2c2d -a2c3d -abc2d2 -ac4d  -ab2cd2 -a2c2d2 -abcd3 -ac|
|  ac3d  0      0     ac3d    ac2d2  0       0      ac2d2   acd3    0      0  |
|  abc3  -ac4   -ac3d a2c2d   abc2d  -ac3d   -ac2d2 a2cd2   abcd2   -ac2d2 -ac|
|  0     a2c3   abc3  0       0      a2c2d   abc2d  0       0       a2cd2  abc|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|, 3}                                                                         |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0   c2d2 0    0    0    cd3 0   0   0   d4 0  0  0  |, {2} | -a2b2 -a3c -a2b|
| 0   0    c2d2 0    0    0   cd3 0   0   0  d4 0  0  |  {3} | a2c   a2d  0   |
| 0   0    0    c2d2 0    0   0   cd3 0   0  0  d4 0  |  {3} | a3    a2b  -a2c|
| c3d 0    0    0    c2d2 0   0   0   cd3 0  0  0  d4 |  {3} | 0     0    a3  |
|                                                                             |
|0    0    0    abd2 0    0    0    ac3 0   0   0   ac2d 0    0    0    acd2 0|
|abcd 0    0    0    abd2 0    0    0   ac3 0   0   0    ac2d 0    0    0    a|
|0    abcd 0    0    0    abd2 0    0   0   ac3 0   0    0    ac2d 0    0    0|
|0    0    abcd 0    0    0    abd2 0   0   0   ac3 0    0    0    ac2d 0    0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|cd-a3c2d a2c3d-ab2cd2 ac4d-abcd3 abcd2-a2d3 ab3d2-a3cd2 a2c2d2-ab2d3 ac3d2-ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-ab4 -a2b2c -ab3d -ab2c2 -ab3c -a2bc2 -ab2cd -abc3 -ab3d -a2bcd -ab2d2 -abc2d|
|ab2c ab2d   0     0      abc2  abcd   0      0     abcd  abd2   0      0     |
|a2b2 ab3    -ab2c -ab2d  a2bc  ab2c   -abc2  -abcd a2bd  ab2d   -abcd  -abd2 |
|0    0      a2b2  ab3    0     0      a2bc   ab2c  0     0      a2bd   ab2d  |
|-----------------------------------------------------------------------------|
|2 b3c3d-a2c4d ac5d-b2c3d2 c6d-bc3d3 bc3d2-ac2d3 b3c2d2-a2c3d2 ac4d2-b2c2d3 c5|
|                                                                             |
|                                                                             |
|3d2 -ab2d3 -a2cd3 -abd4 -ac2d3 -b6 -ab4c -b5d -b4c2 -b5c -ab3c2 -b4cd -b3c3 -|
|    acd3   ad4    0     0      b4c b4d   0    0     b3c2 b3cd   0     0     b|
|d3  a2d3   abd3   -acd3 -ad4   ab4 b5    -b4c -b4d  ab3c b4c    -b3c2 -b3cd a|
|d2  0      0      a2d3  abd3   0   0     ab4  b5    0    0      ab3c  b4c   0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|d -a2c2 -ab3 -a2bc -ab2d -abc2 -ab2c -a2c2 -abcd -ac3 -ab2d -a2cd -abd2 -ac2d|
|  0     abc  abd   0     0     ac2   acd   0     0    acd   ad2   0     0    |
|  -a2d  a2b  ab2   -abc  -abd  a2c   abc   -ac2  -acd a2d   abd   -acd  -ad2 |
|  a2b   0    0     a2b   ab2   0     0     a2c   abc  0     0     a2d   abd  |
|                                                                             |
|    0    0    ad3 0   0   0   b4 0  0  0  b3c 0   0   0   b3d 0   0   0   b2c|
|cd2 0    0    0   ad3 0   0   0  b4 0  0  0   b3c 0   0   0   b3d 0   0   0  |
|    acd2 0    0   0   ad3 0   0  0  b4 0  0   0   b3c 0   0   0   b3d 0   0  |
|    0    acd2 0   0   0   ad3 0  0  0  b4 0   0   0   b3c 0   0   0   b3d 0  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|d4 b4c-ab3d b6-a2b3c ab3c2-b5d b3c3-b4d2 b3c2-ab2cd b5c-a2b2c2 ab2c3-b4cd b2c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| -ab2c2 -a2c3 -abc2d -ac4  -ab2cd -a2c2d -abcd2 -ac3d -ab2d2 -a2cd2 -abd3 -ac|
| ac3    ac2d  0      0     ac2d   acd2   0      0     acd2   ad3    0     0  |
| a2c2   abc2  -ac3   -ac2d a2cd   abcd   -ac2d  -acd2 a2d2   abd2   -acd2 -ad|
| 0      0     a2c2   abc2  0      0      a2cd   abcd  0      0      a2d2  abd|
|-----------------------------------------------------------------------------|
|d2-bc2d4 bc2d3-acd4 b3cd3-a2c2d3 ac3d3-b2cd4 c4d3-bcd5 bcd4-ad5 b3d4-a2cd4 ac|
|                                                                             |
|                                                                             |
|b5d -ab3cd -b4d2 -b3c2d -b4c2 -ab2c3 -b3c2d -b2c4  -b4cd -ab2c2d -b3cd2 -b2c3|
|3cd b3d2   0     0      b2c3  b2c2d  0      0      b2c2d b2cd2   0      0    |
|b3d b4d    -b3cd -b3d2  ab2c2 b3c2   -b2c3  -b2c2d ab2cd b3cd    -b2c2d -b2cd|
|    0      ab3d  b4d    0     0      ab2c2  b3c2   0     0       ab2cd  b3cd |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| -b4 -ab2c -b3d -b2c2 -b3c -abc2 -b2cd -bc3 -b3d -abcd -b2d2 -bc2d -b2c2 -ac3|
| b2c b2d   0    0     bc2  bcd   0     0    bcd  bd2   0     0     c3    c2d |
| ab2 b3    -b2c -b2d  abc  b2c   -bc2  -bcd abd  b2d   -bcd  -bd2  ac2   bc2 |
| 0   0     ab2  b3    0    0     abc   b2c  0    0     abd   b2d   0     0   |
|                                                                             |
|2 0    0    0    b2cd 0    0    0    b2d2 0    0    0    bc3 0   0   0   bc2d|
|  b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0   bc3 0   0   0   |
|  0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0   0   bc3 0   0   |
|  0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0   0   0   bc3 0   |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|4-b3cd2 b3cd-ab2d2 b5d-a2b2cd ab2c2d-b4d2 b2c3d-b3d3 b2c3-abc2d b4c2-a2bc3 ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2d2 -b5 -ab3c -b4d -b3c2 -b4c -ab2c2 -b3cd -b2c3 -b4d -ab2cd -b3d2 -b2c2d -b3|
|    b3c b3d   0    0     b2c2 b2cd   0     0     b2cd b2d2   0     0      bc3|
|3   ab3 b4    -b3c -b3d  ab2c b3c    -b2c2 -b2cd ab2d b3d    -b2cd -b2d2  abc|
|2   0   0     ab3  b4    0    0      ab2c  b3c   0    0      ab2d  b3d    0  |
|-----------------------------------------------------------------------------|
|2d4-b2d5 c3d4-bd6 0 |, | a4bc-a5d a4b3-a6c a5c2-a4b2d a4c3-a4bd2 a3b2c-a4bd a|
|                                                                             |
|                                                                             |
|d -b4d2 -ab2cd2 -b3d3  -b2c2d2 -b3c3 -abc4 -b2c3d -bc5  -b3c2d -abc3d -b2c2d2|
|  b2cd2 b2d3    0      0       bc4   bc3d  0      0     bc3d   bc2d2  0      |
|2 ab2d2 b3d2    -b2cd2 -b2d3   abc3  b2c3  -bc4   -bc3d abc2d  b2c2d  -bc3d  |
|  0     0       ab2d2  b3d2    0     0     abc3   b2c3  0      0      abc2d  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| -bc2d -c4  -b2cd -ac2d -bcd2 -c3d -b2d2 -acd2 -bd3 -c2d2 a4 0  0  0  a3b 0  |
| 0     0    c2d   cd2   0     0    cd2   d3    0    0     0  a4 0  0  0   a3b|
| -c3   -c2d acd   bcd   -c2d  -cd2 ad2   bd2   -cd2 -d3   0  0  a4 0  0   0  |
| ac2   bc2  0     0     acd   bcd  0     0     ad2  bd2   0  0  0  a4 0   0  |
|                                                                             |
| 0    0    0    bcd2 0    0    0    bd3 0   0   0   c4 0  0  0  c3d 0   0   0|
| bc2d 0    0    0    bcd2 0    0    0   bd3 0   0   0  c4 0  0  0   c3d 0   0|
| 0    bc2d 0    0    0    bcd2 0    0   0   bd3 0   0  0  c4 0  0   0   c3d 0|
| 0    0    bc2d 0    0    0    bcd2 0   0   0   bd3 0  0  0  c4 0   0   0   c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|c4-b3c2d bc5-b2c2d2 b2c2d-abcd2 b4cd-a2bc2d abc3d-b3cd2 bc4d-b2cd3 b2cd2-abd3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|c2 -abc3 -b2c2d -bc4  -b3cd -abc2d -b2cd2 -bc3d -b3d2 -abcd2 -b2d3 -bc2d2 -b2|
|   bc2d  0      0     bc2d  bcd2   0      0     bcd2  bd3    0     0      c4 |
|2  b2c2  -bc3   -bc2d abcd  b2cd   -bc2d  -bcd2 abd2  b2d2   -bcd2 -bd3   ac3|
|   0     abc2   b2c2  0     0      abcd   b2cd  0     0      abd2  b2d2   0  |
|-----------------------------------------------------------------------------|
|3b4-a5bc a4bc2-a3b3d a3bc3-a3b2d2 a3bc2-a4cd a3b3c-a5c2 a4c3-a3b2cd a3c4-a3bc|
|                                                                             |
|                                                                             |
| -bc4d  -b3cd2 -abc2d2 -b2cd3 -bc3d2 -b3d3 -abcd3 -b2d4 -bc2d3 -b2c4 -ac5 -bc|
| 0      bc2d2  bcd3    0      0      bcd3  bd4    0     0      c5    c4d  0  |
| -bc2d2 abcd2  b2cd2   -bc2d2 -bcd3  abd3  b2d3   -bcd3 -bd4   ac4   bc4  -c5|
| b2c2d  0      0       abcd2  b2cd2  0     0      abd3  b2d3   0     0    ac4|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0   0   a3c 0   0   0   a3d 0   0   0   a2b2 0    0    0    a2bc 0    0    0|
| 0   0   0   a3c 0   0   0   a3d 0   0   0    a2b2 0    0    0    a2bc 0    0|
| a3b 0   0   0   a3c 0   0   0   a3d 0   0    0    a2b2 0    0    0    a2bc 0|
| 0   a3b 0   0   0   a3c 0   0   0   a3d 0    0    0    a2b2 0    0    0    a|
|                                                                             |
|   c2d2 0    0    0    cd3 0   0   0   d4 0  0  0  |) <----- 0 : {-3, 5}     |
|   0    c2d2 0    0    0   cd3 0   0   0  d4 0  0  |     0                   |
|   0    0    c2d2 0    0   0   cd3 0   0  0  d4 0  |                         |
|3d 0    0    0    c2d2 0   0   0   cd3 0  0  0  d4 |                         |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| b4d2-a2bcd2 abc2d2-b3d3 bc3d2-b2d4 bc4-ac3d b3c3-a2c4 ac5-b2c3d c6-bc3d2 bc3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|c3 -ac4 -bc3d -c5  -b2c2d -ac3d -bc2d2 -c4d  -b2cd2 -ac2d2 -bcd3 -c3d2 -b2d3 |
|   c3d  0     0    c3d    c2d2  0      0     c2d2   cd3    0     0     cd3   |
|   bc3  -c4   -c3d ac2d   bc2d  -c3d   -c2d2 acd2   bcd2   -c2d2 -cd3  ad3   |
|   0    ac3   bc3  0      0     ac2d   bc2d  0      0      acd2  bcd2  0     |
|-----------------------------------------------------------------------------|
|d2 a3bcd-a4d2 a3b3d-a5cd a4c2d-a3b2d2 a3c3d-a3bd3 a2b3c-a3b2d a2b5-a4b2c a3b2|
|                                                                             |
|                                                                             |
|4d -c6  -b2c3d -ac4d -bc3d2 -c5d  -b2c2d2 -ac3d2 -bc2d3 -c4d2 -b2cd3 -ac2d3 -|
|   0    c4d    c3d2  0      0     c3d2    c2d3   0      0     c2d3   cd4    0|
|   -c4d ac3d   bc3d  -c4d   -c3d2 ac2d2   bc2d2  -c3d2  -c2d3 acd3   bcd3   -|
|   bc4  0      0     ac3d   bc3d  0       0      ac2d2  bc2d2 0      0      a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0  |
|    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0  |
|    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d|
|2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|d-ac2d2 b3c2d-a2c3d ac4d-b2c2d2 c5d-bc2d3 bc2d2-acd3 b3cd2-a2c2d2 ac3d2-b2cd3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-acd3 -bd4 -c2d3 0 0 0 0 |, {2} | -a3b2 -a4c -a3bd -a3c2 -a2b3 -a3bc -a2b2d -|
|d4    0    0     0 0 0 0 |  {3} | a3c   a3d  0     0     a2bc  a2bd  0      0|
|bd3   -cd3 -d4   0 0 0 0 |  {3} | a4    a3b  -a3c  -a3d  a3b   a2b2  -a2bc  -|
|0     ad3  bd3   0 0 0 0 |  {3} | 0     0    a4    a3b   0     0     a3b    a|
|-----------------------------------------------------------------------------|
|c2-a2b4d a2b2c3-a2b3d2 a2b2c2-a3bcd a2b4c-a4bc2 a3bc3-a2b3cd a2bc4-a2b2cd2 a2|
|                                                                             |
|                                                                             |
|bcd4 -c3d3 -b2d4 -acd4 -bd5 -c2d4 0 0 0 0 |) <----- 0 : {-5, 6}              |
|     0     cd4   d5    0    0     0 0 0 0 |     0                            |
|c2d3 -cd4  ad4   bd4   -cd4 -d5   0 0 0 0 |                                  |
|cd3  bcd3  0     0     ad4  bd4   0 0 0 0 |                                  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|  0    ab3 0   0   0   ab2c 0    0    0    ab2d 0    0    0    abc2 0    0   |
|  0    0   ab3 0   0   0    ab2c 0    0    0    ab2d 0    0    0    abc2 0   |
|2 0    0   0   ab3 0   0    0    ab2c 0    0    0    ab2d 0    0    0    abc2|
|  a2d2 0   0   0   ab3 0    0    0    ab2c 0    0    0    ab2d 0    0    0   |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| c4d2-bcd4 bcd3-ad4 b3d3-a2cd3 ac2d3-b2d4 c3d3-bd5 0 |) <--------------------|
|                                                           {4} | 1 0 0 0 0 0 |
|                                                           {4} | 0 1 0 0 0 0 |
|                                                           {4} | 0 0 1 0 0 0 |
|                                                           {4} | 0 0 0 1 0 0 |
|                                                           {4} | 0 0 0 0 1 0 |
|                                                           {4} | 0 0 0 0 0 1 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {0} | 0 0 0 0 0 0 |
|                                                                             |
|a2bc2 -a2b2c -a3c2 -a2bcd -a2c3 -a2b2d -a3cd -a2bd2 -a2c2d -ab4 -a2b2c -ab3d |
|      a2c2   a2cd  0      0     a2cd   a2d2  0      0      ab2c ab2d   0     |
|a2bd  a3c    a2bc  -a2c2  -a2cd a3d    a2bd  -a2cd  -a2d2  a2b2 ab3    -ab2c |
|2b2   0      0     a3c    a2bc  0      0     a3d    a2bd   0    0      a2b2  |
|-----------------------------------------------------------------------------|
|b2cd-a3bd2 a2b4d-a4bcd a3bc2d-a2b3d2 a2bc3d-a2b2d3 a2bc3-a3c2d a2b3c2-a4c3 a3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0    abcd 0    0    0    abd2 0    0    0    ac3 0   0   0   ac2d 0    0    |
| 0    0    abcd 0    0    0    abd2 0    0    0   ac3 0   0   0    ac2d 0    |
| 0    0    0    abcd 0    0    0    abd2 0    0   0   ac3 0   0    0    ac2d |
| abc2 0    0    0    abcd 0    0    0    abd2 0   0   0   ac3 0    0    0    |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|------------------------------------------------------------- cokernel {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|                                                                             |
|-ab2c2 -ab3c -a2bc2 -ab2cd -abc3 -ab3d -a2bcd -ab2d2 -abc2d -ab2c2 -a2c3 -abc|
|0      abc2  abcd   0      0     abcd  abd2   0      0      ac3    ac2d  0   |
|-ab2d  a2bc  ab2c   -abc2  -abcd a2bd  ab2d   -abcd  -abd2  a2c2   abc2  -ac3|
|ab3    0     0      a2bc   ab2c  0     0      a2bd   ab2d   0      0     a2c2|
|-----------------------------------------------------------------------------|
|c4-a2b2c2d a2c5-a2bc2d2 a2bc2d-a3cd2 a2b3cd-a4c2d a3c3d-a2b2cd2 a2c4d-a2bcd3 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0    acd2 0    0    0    ad3 0   0   0   b4 0  0  0  b3c 0   0   0   b3d 0   |
|0    0    acd2 0    0    0   ad3 0   0   0  b4 0  0  0   b3c 0   0   0   b3d |
|0    0    0    acd2 0    0   0   ad3 0   0  0  b4 0  0   0   b3c 0   0   0   |
|ac2d 0    0    0    acd2 0   0   0   ad3 0  0  0  b4 0   0   0   b3c 0   0   |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-d -b -d -c 0  0  -d 0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0 |
|c  a  0  0  0  -d 0  -d -b 0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0 |
|0  0  b  a  -d 0  0  0  0  0  -d 0  0  0  0  0  -d -c 0  0  -d 0  0  0  0  0 |
|0  0  0  0  c  b  a  0  0  -d 0  0  0  -d 0  0  0  0  0  -d 0  0  0  -d 0  0 |
|0  0  0  0  0  0  0  c  a  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  -d -b|
|0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  0  0  0  0  0  0  -d 0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  b  a  -d 0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  -d 0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  a |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2d -ac4  -ab2cd -a2c2d -abcd2 -ac3d -ab2d2 -a2cd2 -abd3 -ac2d2 -b5 -ab3c -b4d|
|   0     ac2d   acd2   0      0     acd2   ad3    0     0      b3c b3d   0   |
|   -ac2d a2cd   abcd   -ac2d  -acd2 a2d2   abd2   -acd2 -ad3   ab3 b4    -b3c|
|   abc2  0      0      a2cd   abcd  0      0      a2d2  abd2   0   0     ab3 |
|-----------------------------------------------------------------------------|
|a2bcd2-a3d3 a2b3d2-a4cd2 a3c2d2-a2b2d3 a2c3d2-a2bd4 ab4c-a2b3d ab6-          |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0   0   b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0             |
|0   0   0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0             |
|b3d 0   0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0             |
|0   b3d 0    0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2          |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0            |
| 0  -d 0  0  0  0  0  0  0  -d 0  0  0  0  -d 0  0  0  0  0  0  0            |
| 0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| -d 0  0  0  -d 0  0  0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0            |
| 0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  -d -c 0  0            |
| 0  0  0  0  0  0  0  -d 0  0  0  0  -d 0  0  0  0  0  0  0  0  -d           |
| 0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0  0  0            |
| 0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| d  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  c  b  a  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0            |
| 0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  b  a  -d 0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| -b3c2 -b4c -ab2c2 -b3cd -b2c3 -b4d -ab2cd -b3d2 -b2c2d -b3c2 -abc3          |
| 0     b2c2 b2cd   0     0     b2cd b2d2   0     0      bc3   bc2d           |
| -b3d  ab2c b3c    -b2c2 -b2cd ab2d b3d    -b2cd -b2d2  abc2  b2c2           |
| b4    0    0      ab2c  b3c   0    0      ab2d  b3d    0     0              |
|-----------------------------------------------------------------------------|
|a3b3c a2b3c2-ab5d ab3c3-ab4d2 ab3c2-a2b2cd ab5c-a3b2c2 a2b2c3-ab4cd ab2c4-ab3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| bc3 0   0   0   bc2d 0    0    0    bcd2 0    0    0    bd3 0   0   0   c4 0|
| 0   bc3 0   0   0    bc2d 0    0    0    bcd2 0    0    0   bd3 0   0   0  c|
| 0   0   bc3 0   0    0    bc2d 0    0    0    bcd2 0    0   0   bd3 0   0  0|
| 0   0   0   bc3 0    0    0    bc2d 0    0    0    bcd2 0   0   0   bd3 0  0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  -d 0  0  0  0  -d 0  0 |
|-d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  0 |
|0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  -d 0  0  0  0  -d 0  0  0  0 |
|0  0  0  0  0  0  0  -d -b 0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  -d 0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  -d 0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|a  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  c  b  a  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  c  a  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  0  0  0  0  0  0  0  0  0  -d|
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  d  c  b  a  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| -b2c2d -bc4  -b3cd -abc2d -b2cd2 -bc3d -b3d2 -abcd2 -b2d3 -bc2d2 -b2c3 -ac4 |
| 0      0     bc2d  bcd2   0      0     bcd2  bd3    0     0      c4    c3d  |
| -bc3   -bc2d abcd  b2cd   -bc2d  -bcd2 abd2  b2d2   -bcd2 -bd3   ac3   bc3  |
| abc2   b2c2  0     0      abcd   b2cd  0     0      abd2  b2d2   0     0    |
|-----------------------------------------------------------------------------|
|cd2 ab3cd-a2b2d2 ab5d-a3b2cd a2b2c2d-ab4d2 ab2c3d-ab3d3 ab2c3-a2bc2d ab4c2-  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|  0  0  c3d 0   0   0   c2d2 0    0    0    cd3 0   0   0   d4 0  0  0  |)   |
|4 0  0  0   c3d 0   0   0    c2d2 0    0    0   cd3 0   0   0  d4 0  0  |    |
|  c4 0  0   0   c3d 0   0    0    c2d2 0    0   0   cd3 0   0  0  d4 0  |    |
|  0  c4 0   0   0   c3d 0    0    0    c2d2 0   0   0   cd3 0  0  0  d4 |    |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  -d 0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  -d 0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0   |
| 0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  -d -c 0  0  -d 0  0  0  0   |
| 0  -d 0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  -d 0   |
| 0  0  0  0  0  -d 0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  -d 0  0   |
| 0  0  0  0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| a  0  0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0   |
| 0  d  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  b  a  -d 0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  -d 0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  -d  |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-bc3d -c5  -b2c2d -ac3d -bc2d2 -c4d  -b2cd2 -ac2d2 -bcd3 -c3d2 -b2d3 -acd3   |
|0     0    c3d    c2d2  0      0     c2d2   cd3    0     0     cd3   d4      |
|-c4   -c3d ac2d   bc2d  -c3d   -c2d2 acd2   bcd2   -c2d2 -cd3  ad3   bd3     |
|ac3   bc3  0      0     ac2d   bc2d  0      0      acd2  bcd2  0     0       |
|-----------------------------------------------------------------------------|
|a3bc3 a2bc4-ab3c2d abc5-ab2c2d2 ab2c2d-a2bcd2 ab4cd-a3bc2d a2bc3d-ab3cd2     |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|<----- 0 : {-3, 4}                                                           |
|   0                                                                         |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0  0  0  0  0  c2  -ac 0   0   -cd -ad 0   0   0   -d2 -bd 0   0   0        |
| 0  0  0  0  0  -bd b2  -d2 0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   c2  cd  0   0   0   0   -d2 0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   -d2 0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   -d2 bd  b2  0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   -d2 0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   cd  c2  0   0   0   -d2 0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   -d2      |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   d2  bd  b2  0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   d2  0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   -d2 0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   d2  cd       |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  -d 0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| -d 0  0  0  -d 0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  -d 0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| b  a  -d 0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  c  b  a  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-bd4 -c2d3 0 0 0 0 |) <----- 0 : {-4, 5}                                     |
|0    0     0 0 0 0 |     0                                                   |
|-cd3 -d4   0 0 0 0 |                                                         |
|ad3  bd3   0 0 0 0 |                                                         |
|-----------------------------------------------------------------------------|
| abc4d-ab2cd3 ab2cd2-a2bd3 ab4d2-a3bcd2 a2bc2d2-ab3d3 abc3d2-ab2d4 abc4-a2c3d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0   0   0   0   0   0   0   0   0   0   | : {-4, 4}                          |
|0   0   -d2 -bd 0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   -d2 0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|-d2 0   0   0   -d2 0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|c2  0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   -d2 0   0   -d2 0   |                                    |
|0   0   0   0   0   0   0   -d2 0   0   |                                    |
|0   0   0   0   0   0   -d2 0   0   0   |                                    |
|0   d2  bd  b2  0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   d2  0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   d2  0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   -d2 |                                    |
|0   0   0   0   0   0   d2  cd  c2  0   |                                    |
|0   0   0   0   0   0   0   0   0   d2  |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|-----------------------------------------------------------------------------|
|ab3c3-a3c4 a2c5-ab2c3d ac6-abc3d2 abc3d-a2c2d2 ab3c2d-a3c3d a2c4d-ab2c2d2    |
|                                                                             |
|-----------------------------------------------------------------------------|
|ac5d-abc2d3 abc2d2-a2cd3 ab3cd2-a3c2d2 a2c3d2-ab2cd3 ac4d2-abcd4 abcd3-a2d4  |
|                                                                             |
|-----------------------------------------------------------------------------|
|ab3d3-a3cd3 a2c2d3-ab2d4 ac3d3-abd5 b5c-ab4d b7-a2b4c ab4c2-b6d b4c3-b5d2    |
|                                                                             |
|-----------------------------------------------------------------------------|
|b4c2-ab3cd b6c-a2b3c2 ab3c3-b5cd b3c4-b4cd2 b4cd-ab3d2 b6d-a2b3cd ab3c2d-b5d2|
|                                                                             |
|-----------------------------------------------------------------------------|
|b3c3d-b4d3 b3c3-ab2c2d b5c2-a2b2c3 ab2c4-b4c2d b2c5-b3c2d2 b3c2d-ab2cd2      |
|                                                                             |
|-----------------------------------------------------------------------------|
|b5cd-a2b2c2d ab2c3d-b4cd2 b2c4d-b3cd3 b3cd2-ab2d3 b5d2-a2b2cd2 ab2c2d2-b4d3  |
|                                                                             |
|-----------------------------------------------------------------------------|
|b2c3d2-b3d4 b2c4-abc3d b4c3-a2bc4 abc5-b3c3d bc6-b2c3d2 b2c3d-abc2d2         |
|                                                                             |
|-----------------------------------------------------------------------------|
|b4c2d-a2bc3d abc4d-b3c2d2 bc5d-b2c2d3 b2c2d2-abcd3 b4cd2-a2bc2d2 abc3d2-b3cd3|
|                                                                             |
|-----------------------------------------------------------------------------|
|bc4d2-b2cd4 b2cd3-abd4 b4d3-a2bcd3 abc2d3-b3d4 bc3d3-b2d5 bc5-ac4d b3c4-a2c5 |
|                                                                             |
|-----------------------------------------------------------------------------|
|ac6-b2c4d c7-bc4d2 bc4d-ac3d2 b3c3d-a2c4d ac5d-b2c3d2 c6d-bc3d3 bc3d2-ac2d3  |
|                                                                             |
|-----------------------------------------------------------------------------|
|b3c2d2-a2c3d2 ac4d2-b2c2d3 c5d2-bc2d4 bc2d3-acd4 b3cd3-a2c2d3 ac3d3-b2cd4    |
|                                                                             |
|-----------------------------------------------------------------------------|
|c4d3-bcd5 bcd4-ad5 b3d4-a2cd4 ac2d4-b2d5 c3d4-bd6 0 |) <----- 0 : {-5, 5}    |
|                                                          0                  |
+-----------------------------------------------------------------------------+

See also
========

  * prune(SpectralSequence),
    -- a minimal presentation of a spectral sequence
  * SpectralSequencePage -- the type of all
    spectral sequence pages
  * PageMap -- the type of all page maps

Ways to use pruningMaps:
========================

  * pruningMaps(SpectralSequencePage)
    -- compute the pruning maps on a
    spectral sequence page

For the programmer
==================

The object pruningMaps, is a method function (Macaulay2Doc).

-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2801:0.

pruningMaps(SpectralSequencePage) -- compute the pruning maps on a spectral sequence page
*****************************************************************************************

  * Function: pruningMaps,

Description
===========

Returns the pruning maps which are cached in the process of pruning the
spectral sequence page.

As a specific example consider the filtered complex $K$ below, obtained by
multiplying the minimal free resolution of the rational quartic space curve by
successive powers of the irrelevant ideal.

+----------------------------------------------------+
|i1 : B = QQ[a..d];                                  |
+----------------------------------------------------+
|i2 : J = ideal vars B;                              |
|                                                    |
|o2 : Ideal of B                                     |
+----------------------------------------------------+
|i3 : C = complete res monomialCurveIdeal(B,{1,3,4});|
+----------------------------------------------------+
|i4 : K = filteredComplex(J,C,4);                    |
+----------------------------------------------------+

We compute an example of a pruning map below.

+-----------------------------------------------------------------------------+
|i5 : E = prune spectralSequence K;                                           |
+-----------------------------------------------------------------------------+
|i6 : pruningMaps E^2                                                         |
|                                                                             |
|o6 = {-7, 6} : subquotient (| 0 a4bc-a5d a4b3-a6c a5c2-a4b2d a4c3-a4bd2 a3b2c|
|                                                                             |
|                                                                             |
|     {-7, 7} : subquotient ({2} | 0 0 0 0 -a4b2 -a5c -a4bd -a4c2 -a3b3 -a4bc |
|                            {3} | 0 0 0 0 a4c   a4d  0     0     a3bc  a3bd  |
|                            {3} | 0 0 0 0 a5    a4b  -a4c  -a4d  a4b   a3b2  |
|                            {3} | 0 0 0 0 0     0    a5    a4b   0     0     |
|                                                                             |
|     {-7, 8} : subquotient ({4} | 0 0 0 0 a4d  a3bd  a3cd  a3d2  a2b2d  a2bcd|
|                            {4} | 0 0 0 0 -a4c -a3bc -a3c2 -a3cd -a2b2c -a2bc|
|                            {4} | 0 0 0 0 -a4b -a3b2 -a3bc -a3bd -a2b3  -a2b2|
|                            {4} | 0 0 0 0 a5   a4b   a4c   a4d   a3b2   a3bc |
|                                                                             |
|     {-7, 9} : image 0 <----- 0 : {-5, 8}                                    |
|                          0                                                  |
|                                                                             |
|     {-7, 10} : 0 <----- 0 : {-5, 9}                                         |
|                     0                                                       |
|                                                                             |
|     {-2, 1} : cokernel | bc-ad b3-a2c ac2-b2d c3-bd2 a b c d | <--------- co|
|                                                                   | 1 |     |
|                                                                             |
|     {-2, 2} : cokernel {2} | -b2 -ac -bd -c2 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0|
|                        {3} | c   d   0   0   0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0|
|                        {3} | a   b   -c  -d  0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0|
|                        {3} | 0   0   a   b   0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d|
|                                                                             |
|                                                                             |
|     {-2, 3} : subquotient ({4} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 d  a 0 0 0 |
|                            {4} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 -c 0 a 0 0 |
|                            {4} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 -b 0 0 a 0 |
|                            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a a  0 0 0 a |
|                                                                             |
|     {-2, 4} : subquotient ({5} | d c b a a b c d |, {5} | a b c d |) <----- |
|                                                                         0   |
|                                                                             |
|     {-2, 5} : 0 <----- 0 : {0, 4}                                           |
|                    0                                                        |
|                                                                             |
|     {-3, 2} : subquotient (| a b c d bc-ad b3-a2c ac2-b2d c3-bd2 a2 ab ac ad|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|     {-3, 3} : subquotient ({2} | a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 -b2 -ac -bd|
|                            {3} | 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 c   d   0  |
|                            {3} | 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 a   b   -c |
|                            {3} | 0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0   0   a  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|     {-3, 4} : subquotient ({4} | d  ad ac ab a2 0  0  0  0  0  0  0  0  0  0|
|                            {4} | -c 0  0  0  0  ad ac ab a2 0  0  0  0  0  0|
|                            {4} | -b 0  0  0  0  0  0  0  0  ad ac ab a2 0  0|
|                            {4} | a  0  0  0  0  0  0  0  0  0  0  0  0  ad a|
|                                                                             |
|     {-3, 5} : subquotient ({5} | ad ac ab a2 bd bc b2 ab cd c2 bc ac d2 cd b|
|                                                                             |
|                                                                             |
|     {-3, 6} : 0 <----- 0 : {-1, 5}                                          |
|                    0                                                        |
|                                                                             |
|     {-4, 3} : subquotient (| a2 ab ac ad b2 bc bd c2 cd d2 abc-a2d ab3-a3c a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|     {-4, 4} : subquotient ({2} | a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0|
|                            {3} | 0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0|
|                            {3} | 0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  a|
|                            {3} | 0  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|     {-4, 5} : subquotient ({4} | ad  bd  cd  d2  a2d a2c a2b a3 0   0   0   |
|                            {4} | -ac -bc -c2 -cd 0   0   0   0  a2d a2c a2b |
|                            {4} | -ab -b2 -bc -bd 0   0   0   0  0   0   0   |
|                            {4} | a2  ab  ac  ad  0   0   0   0  0   0   0   |
|                                                                             |
|     {-4, 6} : subquotient ({5} | a2d a2c a2b a3 abd abc ab2 a2b acd ac2 abc |
|                                                                             |
|                                                                             |
|     {-4, 7} : 0 <----- 0 : {-2, 6}                                          |
|                    0                                                        |
|                                                                             |
|     {-5, 4} : subquotient (| a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3 b2c b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|     {-5, 5} : subquotient ({2} | 0 a2b2 a2bd a2bd 0 a3c  a3c  a2c2 a2b2 ab3 |
|                            {3} | 0 -a2c 0    0    0 -a2d -a2d 0    -a2c -abc|
|                            {3} | 0 -a3  a2c  a2c  0 -a2b -a2b a2d  -a3  -a2b|
|                            {3} | 0 0    -a3  -a3  0 0    0    -a2b 0    0   |
|                                                                             |
|     {-5, 6} : subquotient ({4} | a2d  abd  acd  ad2  b2d  bcd  bd2  c2d  cd2|
|                            {4} | -a2c -abc -ac2 -acd -b2c -bc2 -bcd -c3  -c2|
|                            {4} | -a2b -ab2 -abc -abd -b3  -b2c -b2d -bc2 -bc|
|                            {4} | a3   a2b  a2c  a2d  ab2  abc  abd  ac2  acd|
|                                                                             |
|     {-5, 7} : subquotient ({5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                                                                             |
|                                                                             |
|     {-5, 8} : 0 <----- 0 : {-3, 7}                                          |
|                    0                                                        |
|                                                                             |
|     {-6, 5} : subquotient (| a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|     {-6, 6} : subquotient ({2} | 0 a3b2 a3bd a3bd 0 a4c  a4c  a3c2 a3b2 a2b3|
|                            {3} | 0 -a3c 0    0    0 -a3d -a3d 0    -a3c -a2b|
|                            {3} | 0 -a4  a3c  a3c  0 -a3b -a3b a3d  -a4  -a3b|
|                            {3} | 0 0    -a4  -a4  0 0    0    -a3b 0    0   |
|                                                                             |
|     {-6, 7} : subquotient ({4} | a3d  a2bd  a2cd  a2d2  ab2d  abcd  abd2  ac|
|                            {4} | -a3c -a2bc -a2c2 -a2cd -ab2c -abc2 -abcd -a|
|                            {4} | -a3b -a2b2 -a2bc -a2bd -ab3  -ab2c -ab2d -a|
|                            {4} | a4   a3b   a3c   a3d   a2b2  a2bc  a2bd  a2|
|                                                                             |
|     {-6, 8} : image 0 <----- 0 : {-4, 7}                                    |
|                          0                                                  |
|                                                                             |
|     {-6, 9} : 0 <----- 0 : {-4, 8}                                          |
|                    0                                                        |
|                                                                             |
|o6 : PageMap                                                                 |
|-----------------------------------------------------------------------------|
|-a4bd a3b4-a5bc a4bc2-a3b3d a3bc3-a3b2d2 a3bc2-a4cd a3b3c-a5c2 a4c3-a3b2cd a3|
|                                                                             |
|                                                                             |
|-a3b2d -a3bc2 -a3b2c -a4c2 -a3bcd -a3c3 -a3b2d -a4cd -a3bd2 -a3c2d -a2b4 -a3b|
|0      0      a3c2   a3cd  0      0     a3cd   a3d2  0      0      a2b2c a2b2|
|-a3bc  -a3bd  a4c    a3bc  -a3c2  -a3cd a4d    a3bd  -a3cd  -a3d2  a3b2  a2b3|
|a4b    a3b2   0      0     a4c    a3bc  0      0     a4d    a3bd   0     0   |
|                                                                             |
|  a2bd2  a2c2d  a2cd2  a2d3   ab3d  ab2cd  ab2d2  abc2d  abcd2  abd3   ac3d  |
|2 -a2bcd -a2c3  -a2c2d -a2cd2 -ab3c -ab2c2 -ab2cd -abc3  -abc2d -abcd2 -ac4  |
|c -a2b2d -a2bc2 -a2bcd -a2bd2 -ab4  -ab3c  -ab3d  -ab2c2 -ab2cd -ab2d2 -abc3 |
|  a3bd   a3c2   a3cd   a3d2   a2b3  a2b2c  a2b2d  a2bc2  a2bcd  a2bd2  a2c3  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|kernel | d c b a | : {0, 0}                                                  |
|                                                                             |
|                                                                             |
| | <------------------- cokernel {2} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 | : {0|
| |    {2} | 1 0 0 0 |            {3} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 |     |
| |    {3} | 0 1 0 0 |            {3} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 |     |
| |    {3} | 0 0 1 0 |            {3} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a |     |
|      {3} | 0 0 0 1 |                                                        |
|                                                                             |
|b 0 0 0 c 0 0 0 d 0 0 0 |, {4} | d  a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 |) <-----|
|0 b 0 0 0 c 0 0 0 d 0 0 |  {4} | -c 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 |     0  |
|0 0 b 0 0 0 c 0 0 0 d 0 |  {4} | -b 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 |        |
|0 0 0 b 0 0 0 c 0 0 0 d |  {4} | a  0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d |        |
|                                                                             |
|0 : {0, 3}                                                                   |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| b2 bc bd c2 cd d2 |, | bc-ad b3-a2c ac2-b2d c3-bd2 a2 ab ac ad b2 bc bd c2 c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| -c2 a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  |
| 0   0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  |
| -d  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  |
| b   0  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|  0  0  bd bc b2 ab 0  0  0  0  0  0  0  0  0  0  0  0  cd c2 bc ac 0  0  0  |
|  0  0  0  0  0  0  bd bc b2 ab 0  0  0  0  0  0  0  0  0  0  0  0  cd c2 bc |
|  0  0  0  0  0  0  0  0  0  0  bd bc b2 ab 0  0  0  0  0  0  0  0  0  0  0  |
|c ab a2 0  0  0  0  0  0  0  0  0  0  0  0  bd bc b2 ab 0  0  0  0  0  0  0  |
|                                                                             |
|d ad a2 ab ac ad b2 bc bd c2 cd d2 |, {5} | a2 ab ac ad b2 bc bd c2 cd d2 |) |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2c2-ab2d ac3-abd2 b2c-abd b4-a2bc abc2-b3d bc3-b2d2 bc2-acd b3c-a2c2 ac3-b2cd|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |
|  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |
|d 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |
|  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0  0   0   0   0  0   0   0   0  abd abc ab2 a2b 0   0   0   0   0   0   0   |
|a3 0   0   0   0  0   0   0   0  0   0   0   0   abd abc ab2 a2b 0   0   0   |
|0  a2d a2c a2b a3 0   0   0   0  0   0   0   0   0   0   0   0   abd abc ab2 |
|0  0   0   0   0  a2d a2c a2b a3 0   0   0   0   0   0   0   0   0   0   0   |
|                                                                             |
|a2c ad2 acd abd a2d b2d b2c b3 ab2 bcd bc2 b2c abc bd2 bcd b2d abd c2d c3 bc2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2d bc2 bcd bd2 c3 c2d cd2 d3 a2bc-a3d a2b3-a4c a3c2-a2b2d a2c3-a2bd2 ab2c-a2b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| ab2d ab2d a2bd a2bc a2bc a2bc abc2 abc2 a2c2 ab2c ab2c abcd abcd abcd 0     |
| 0    0    0    -abd -abd -abd 0    0    0    -ac2 -ac2 0    0    0    acd   |
| abc  abc  a2c  -ab2 -ab2 -ab2 abd  abd  a2d  -a2c -a2c ac2  ac2  ac2  abc+a2|
| -a2b -a2b -a3  0    0    0    -ab2 -ab2 -a2b 0    0    -a2c -a2c -a2c -a2b  |
|                                                                             |
|  d3   a3d  0 0 -a2bd 0 0 0 0 -a2cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -ab2d -|
|d -cd2 -a3c 0 0 a2bc  0 0 0 0 a2c2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ab2c  a|
|d -bd2 -a3b 0 0 a2b2  0 0 0 0 a2bc  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ab3   a|
|  ad2  a4   0 0 -a3b  0 0 0 0 -a3c  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a2b2 -|
|                                                                             |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a4 a3b a3c a3d a2b2 a2bc a2bd |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|3 ab2c ab2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|  a2b2d a2b2d a3bd a3bc  a3bc  a3bc  a2bc2 a2bc2 a3c2 a2b2c a2b2c a2bcd a2bcd|
|c 0     0     0    -a2bd -a2bd -a2bd 0     0     0    -a2c2 -a2c2 0     0    |
|  a2bc  a2bc  a3c  -a2b2 -a2b2 -a2b2 a2bd  a2bd  a3d  -a3c  -a3c  a2c2  a2c2 |
|  -a3b  -a3b  -a4  0     0     0     -a2b2 -a2b2 -a3b 0     0     -a3c  -a3c |
|                                                                             |
|2d  acd2  ad3   b3d  b2cd  b2d2  bc2d  bcd2  bd3   c3d  c2d2  cd3   d4   a4d |
|c3  -ac2d -acd2 -b3c -b2c2 -b2cd -bc3  -bc2d -bcd2 -c4  -c3d  -c2d2 -cd3 -a4c|
|bc2 -abcd -abd2 -b4  -b3c  -b3d  -b2c2 -b2cd -b2d2 -bc3 -bc2d -bcd2 -bd3 -a4b|
|c2  a2cd  a2d2  ab3  ab2c  ab2d  abc2  abcd  abd2  ac3  ac2d  acd2  ad3  a5  |
|-----------------------------------------------------------------------------|
|c4-a3bcd2 a3bcd-a4d2 a3b3d-a5cd a4c2d-a3b2d2 a3c3d-a3bd3 a2b3c-a3b2d a2b5-a4b|
|                                                                             |
|                                                                             |
|2c -a2b3d -a2b2c2 -a2b3c -a3bc2 -a2b2cd -a2bc3 -a2b3d -a3bcd -a2b2d2 -a2bc2d |
|d  0      0       a2bc2  a2bcd  0       0      a2bcd  a2bd2  0       0       |
|   -a2b2c -a2b2d  a3bc   a2b2c  -a2bc2  -a2bcd a3bd   a2b2d  -a2bcd  -a2bd2  |
|   a3b2   a2b3    0      0      a3bc    a2b2c  0      0      a3bd    a2b2d   |
|                                                                             |
|ac2d2  acd3   ad4   b4d  b3cd  b3d2  b2c2d b2cd2  b2d3   bc3d  bc2d2  bcd3   |
|-ac3d  -ac2d2 -acd3 -b4c -b3c2 -b3cd -b2c3 -b2c2d -b2cd2 -bc4  -bc3d  -bc2d2 |
|-abc2d -abcd2 -abd3 -b5  -b4c  -b4d  -b3c2 -b3cd  -b3d2  -b2c3 -b2c2d -b2cd2 |
|a2c2d  a2cd2  a2d3  ab4  ab3c  ab3d  ab2c2 ab2cd  ab2d2  abc3  abc2d  abcd2  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|, 1}                                                                         |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0 : {0, 2}                                                                  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|d d2 |) <------------------- cokernel {1} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 ||
|           {1} | 1 0 0 0 |            {1} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 ||
|           {1} | 0 1 0 0 |            {1} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 ||
|           {1} | 0 0 1 0 |            {1} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a ||
|           {1} | 0 0 0 1 |                                                   |
|           {2} | 0 0 0 0 |                                                   |
|           {3} | 0 0 0 0 |                                                   |
|           {3} | 0 0 0 0 |                                                   |
|           {3} | 0 0 0 0 |                                                   |
|           {2} | 0 0 0 0 |                                                   |
|           {2} | 0 0 0 0 |                                                   |
|           {2} | 0 0 0 0 |                                                   |
|           {2} | 0 0 0 0 |                                                   |
|           {2} | 0 0 0 0 |                                                   |
|           {2} | 0 0 0 0 |                                                   |
|           {2} | 0 0 0 0 |                                                   |
|           {2} | 0 0 0 0 |                                                   |
|           {2} | 0 0 0 0 |                                                   |
|           {2} | 0 0 0 0 |                                                   |
|                                                                             |
|bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |, {2} | -b2 -ac -bd -c2 a2 0|
|0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |  {3} | c   d   0   0   0  a|
|0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |  {3} | a   b   -c  -d  0  0|
|0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |  {3} | 0   0   a   b   0  0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  d  a2 0  0  0 |
|ac 0  0  0  0  0  0  0  0  d2 cd bd ad 0  0  0  0  0  0  0  0  -c 0  a2 0  0 |
|0  cd c2 bc ac 0  0  0  0  0  0  0  0  d2 cd bd ad 0  0  0  0  -b 0  0  a2 0 |
|0  0  0  0  0  cd c2 bc ac 0  0  0  0  0  0  0  0  d2 cd bd ad a  0  0  0  a2|
|                                                                             |
|<----- 0 : {-1, 4}                                                           |
|   0                                                                         |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| c4-bcd2 bcd-ad2 b3d-a2cd ac2d-b2d2 c3d-bd3 a3 a2b a2c a2d ab2 abc abd ac2 ac|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-ab2 -a2c -abd -ac2 -b3 -abc -b2d -bc2 -b2c -ac2 -bcd -c3 -b2d -acd -bd2 -c2d|
|ac   ad   0    0    bc  bd   0    0    c2   cd   0    0   cd   d2   0    0   |
|a2   ab   -ac  -ad  ab  b2   -bc  -bd  ac   bc   -c2  -cd ad   bd   -cd  -d2 |
|0    0    a2   ab   0   0    ab   b2   0    0    ac   bc  0    0    ad   bd  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0   0   0   0   0   acd ac2 abc a2c 0   0   0   0   0   0   0   0   0   0   0|
|0   0   0   0   0   0   0   0   0   acd ac2 abc a2c 0   0   0   0   0   0   0|
|a2b 0   0   0   0   0   0   0   0   0   0   0   0   acd ac2 abc a2c 0   0   0|
|0   abd abc ab2 a2b 0   0   0   0   0   0   0   0   0   0   0   0   acd ac2 a|
|                                                                             |
| ac2 cd2 c2d bcd acd d3 cd2 bd2 ad2 a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|d ab4-a3bc a2bc2-ab3d abc3-ab2d2 abc2-a2cd ab3c-a3c2 a2c3-ab2cd ac4-abcd2 abc|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|  abd2 ac3  abd2 0 a2cd a2cd a2cd ac2d ac2d ab3  ab2c b4   b3d  b3d  ab2d 0  |
|  0    0    0    0 -ad2 -ad2 -ad2 0    0    -abc -ac2 -b2c 0    0    0    -ac|
|d acd  acd  acd  0 -abd -abd -abd ad2  ad2  -a2b -a2c -ab2 b2c  b2c  abc  b3-|
|  -a2d -abc -a2d 0 0    0    0    -abd -abd 0    0    0    -ab2 -ab2 -a2b 0  |
|                                                                             |
|a2bd 0 0 0 -abcd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -ac2d -abcd -a2cd 0 0 0 0 |
|2bc  0 0 0 abc2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ac3   abc2  a2c2  0 0 0 0 |
|2b2  0 0 0 ab2c  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 abc2  ab2c  a2bc  0 0 0 0 |
|a3b  0 0 0 -a2bc 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a2c2 -a2bc -a3c  0 0 0 0 |
|                                                                             |
|a2c2 a2cd a2d2 ab3 ab2c ab2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2d bcd2 bd3 c4 c3d c2d2 cd3 d4 a3bc-a4d a3b3-a5c a4c2-a3b2d a3c3-a3bd2 a2b2c-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| a2bcd 0        a2bd2 a2c3  a2bd2 0 a3cd  a3cd  a3cd  a2c2d a2c2d a2b3  a2b2c|
| 0     a2cd     0     0     0     0 -a2d2 -a2d2 -a2d2 0     0     -a2bc -a2c2|
| a2c2  a2bc+a3d a2cd  a2cd  a2cd  0 -a2bd -a2bd -a2bd a2d2  a2d2  -a3b  -a3c |
| -a3c  -a3b     -a3d  -a2bc -a3d  0 0     0     0     -a2bd -a2bd 0     0    |
|                                                                             |
| 0 0 -a3bd 0 0 0 0 -a3cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a2b2d -a3bd 0 0 0|
| 0 0 a3bc  0 0 0 0 a3c2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a2b2c  a3bc  0 0 0|
| 0 0 a3b2  0 0 0 0 a3bc  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a2b3   a3b2  0 0 0|
| 0 0 -a4b  0 0 0 0 -a4c  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a3b2  -a4b  0 0 0|
|-----------------------------------------------------------------------------|
|2c a3b2c2-a2b4d a2b2c3-a2b3d2 a2b2c2-a3bcd a2b4c-a4bc2 a3bc3-a2b3cd a2bc4-a2b|
|                                                                             |
|                                                                             |
|-a2b2c2 -a3c3 -a2bc2d -a2c4  -a2b2cd -a3c2d -a2bcd2 -a2c3d -a2b2d2 -a3cd2 -a2|
|a2c3    a2c2d 0       0      a2c2d   a2cd2  0       0      a2cd2   a2d3   0  |
|a3c2    a2bc2 -a2c3   -a2c2d a3cd    a2bcd  -a2c2d  -a2cd2 a3d2    a2bd2  -a2|
|0       0     a3c2    a2bc2  0       0      a3cd    a2bcd  0       0      a3d|
|                                                                             |
|bd4   c4d  c3d2  c2d3   cd4   d5   0 0 0 0 |, {4} | a4d  a3bd  a3cd  a3d2  a2|
|-bcd3 -c5  -c4d  -c3d2  -c2d3 -cd4 0 0 0 0 |  {4} | -a4c -a3bc -a3c2 -a3cd -a|
|-b2d3 -bc4 -bc3d -bc2d2 -bcd3 -bd4 0 0 0 0 |  {4} | -a4b -a3b2 -a3bc -a3bd -a|
|abd3  ac4  ac3d  ac2d2  acd3  ad4  0 0 0 0 |  {4} | a5   a4b   a4c   a4d   a3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| : {-1, 1}                                                                   |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  |
|2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  |
|  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd |
|  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0|
| 0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c|
| 0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0|
| 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|d ad2 b3 b2c b2d bc2 bcd bd2 c3 c2d cd2 d3 |, | abc-a2d ab3-a3c a2c2-ab2d ac3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   |
| 0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   |
| 0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   |
| 0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|   0   0   0   0   0   0   0   0   0   0   0   0   0   b2d b2c b3 ab2 0   0  |
|   0   ad2 acd abd a2d 0   0   0   0   0   0   0   0   0   0   0  0   b2d b2c|
|   0   0   0   0   0   ad2 acd abd a2d 0   0   0   0   0   0   0  0   0   0  |
|bc a2c 0   0   0   0   0   0   0   0   ad2 acd abd a2d 0   0   0  0   0   0  |
|                                                                             |
| b2c b2d bc2 bcd bd2 c3 c2d cd2 d3 |, {5} | a3 a2b a2c a2d ab2 abc abd ac2 ac|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|d-a2d2 ab3d-a3cd a2c2d-ab2d2 ac3d-abd3 b3c-ab2d b5-a2b2c ab2c2-b4d b2c3-b3d2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|      b2c2 b2c2 abc2 b3c  b3c  b2cd b2cd b2cd abcd 0       b2d2 bc3  b2d2 abd|
|2+b2d 0    0    0    -bc2 -bc2 0    0    0    0    bcd     0    0    0    0  |
|a2c   b2d  b2d  abd  -abc -abc bc2  bc2  bc2  ac2  b2c+abd bcd  bcd  bcd  acd|
|      -b3  -b3  -ab2 0    0    -abc -abc -abc -a2c -ab2    -abd -b2c -abd -a2|
|                                                                             |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -b3d -ab2d 0 0 0 -b2cd 0 0 0 0 0 0 0 |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b3c  ab2c  0 0 0 b2c2  0 0 0 0 0 0 0 |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b4   ab3   0 0 0 b3c   0 0 0 0 0 0 0 |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -ab3 -a2b2 0 0 0 -ab2c 0 0 0 0 0 0 0 |
|                                                                             |
| b2cd b2d2 bc3 bc2d bcd2 bd3 c4 c3d c2d2 cd3 d4 |, {5} | a4 a3b a3c a3d a2b2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|a3bd a2b4-a4bc a3bc2-a2b3d a2bc3-a2b2d2 a2bc2-a3cd a2b3c-a4c2 a3c3-a2b2cd a2c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| ab4   ab3d  ab3d  a2b2d 0          ab2c2 ab2c2 a2bc2 ab3c  ab3c  ab2cd ab2cd|
| -ab2c 0     0     0     -a2c2+ab2d 0     0     0     -abc2 -abc2 0     0    |
| -a2b2 ab2c  ab2c  a2bc  ab3-a3c    ab2d  ab2d  a2bd  -a2bc -a2bc abc2  abc2 |
| 0     -a2b2 -a2b2 -a3b  0          -ab3  -ab3  -a2b2 0     0     -a2bc -a2bc|
|                                                                             |
| -a2bcd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a2c2d -a2bcd -a3cd 0 0 0 0 0 0 0 0|
| a2bc2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a2c3   a2bc2  a3c2  0 0 0 0 0 0 0 0|
| a2b2c  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a2bc2  a2b2c  a3bc  0 0 0 0 0 0 0 0|
| -a3bc  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a3c2  -a3bc  -a4c  0 0 0 0 0 0 0 0|
|-----------------------------------------------------------------------------|
|2cd2 a2b2cd-a3bd2 a2b4d-a4bcd a3bc2d-a2b3d2 a2bc3d-a2b2d3 a2bc3-a3c2d a2b3c2-|
|                                                                             |
|                                                                             |
|bd3 -a2c2d2 -ab5 -a2b3c -ab4d -ab3c2 -ab4c -a2b2c2 -ab3cd -ab2c3 -ab4d -a2b2c|
|    0       ab3c ab3d   0     0      ab2c2 ab2cd   0      0      ab2cd ab2d2 |
|cd2 -a2d3   a2b3 ab4    -ab3c -ab3d  a2b2c ab3c    -ab2c2 -ab2cd a2b2d ab3d  |
|2   a2bd2   0    0      a2b3  ab4    0     0       a2b2c  ab3c   0     0     |
|                                                                             |
|b2d  a2bcd  a2bd2  a2c2d  a2cd2  a2d3   ab3d  ab2cd  ab2d2  abc2d  abcd2  abd|
|2b2c -a2bc2 -a2bcd -a2c3  -a2c2d -a2cd2 -ab3c -ab2c2 -ab2cd -abc3  -abc2d -ab|
|2b3  -a2b2c -a2b2d -a2bc2 -a2bcd -a2bd2 -ab4  -ab3c  -ab3d  -ab2c2 -ab2cd -ab|
|b2   a3bc   a3bd   a3c2   a3cd   a3d2   a2b3  a2b2c  a2b2d  a2bc2  a2bcd  a2b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |) <----------------------------------|
|0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |     {3} | 1 0 0 0 0 0  0 0 0 0  0 0 |
|0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |     {4} | 0 1 0 0 0 0  0 0 0 0  0 0 |
|bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |     {4} | 0 0 0 0 0 -1 0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  1 0 0 0  0 0 |
|                                             {3} | 0 0 1 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 1 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 -1 0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  1 0 |
|                                             {3} | 0 0 0 0 1 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 1 0 0  0 0 |
|                                             {3} | 0 0 0 0 0 0  0 0 1 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 1 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                             {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
|                                                                             |
|  0  0  cd 0  0  0  d2 0  0  0  |, {4} | d  a2 0  0  0  ab 0  0  0  ac 0  0  |
|2 0  0  0  cd 0  0  0  d2 0  0  |  {4} | -c 0  a2 0  0  0  ab 0  0  0  ac 0  |
|  c2 0  0  0  cd 0  0  0  d2 0  |  {4} | -b 0  0  a2 0  0  0  ab 0  0  0  ac |
|  0  c2 0  0  0  cd 0  0  0  d2 |  {4} | a  0  0  0  a2 0  0  0  ab 0  0  0  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-abd2 b2c-abd b4-a2bc abc2-b3d bc3-b2d2 bc2-acd b3c-a2c2 ac3-b2cd c4-bcd2 bcd|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0|
|0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0|
|0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0|
|0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0  0   0   0   0  0   0   0   0  0   bcd bc2 b2c abc 0   0   0   0   0   0  |
| b3 ab2 0   0   0  0   0   0   0  0   0   0   0   0   bcd bc2 b2c abc 0   0  |
| 0  0   b2d b2c b3 ab2 0   0   0  0   0   0   0   0   0   0   0   0   bcd bc2|
| 0  0   0   0   0  0   b2d b2c b3 ab2 0   0   0   0   0   0   0   0   0   0  |
|                                                                             |
|d ad2 b3 b2c b2d bc2 bcd bd2 c3 c2d cd2 d3 |) <----- 0 : {-2, 5}             |
|                                                 0                           |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|b2c2-abcd b4c-a2bc2 abc3-b3cd bc4-b2cd2 b2cd-abd2 b4d-a2bcd abc2d-b3d2 bc3d-b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2 0       bc2d bc2d bc3  ac3  0       0        bc2d ac2d 0       bcd2 bcd2 c4|
|  bd2     0    0    0    0    c3      0        0    0    c2d     0    0    0 |
|  ac2+b2d bd2  bd2  bcd  acd  ac2+b2d c3-bd2   bd2  ad2  bc2+acd c2d  c2d  c2|
|d -a2c    -b2d -b2d -b2c -abc -b3     -ac2+b2d -b2d -abd -abc    -acd -acd -b|
|                                                                             |
|0 0 0 0 0 0 0 0 0 0 -bc2d -b2cd -abcd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 bc3   b2c2  abc2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 b2c2  b3c   ab2c  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 -abc2 -ab2c -a2bc 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                                                                             |
|a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|4-a2bcd2 a2bcd-a3d2 a2b3d-a4cd a3c2d-a2b2d2 a2c3d-a2bd3 ab3c-a2b2d ab5-a3b2c |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| ab2cd a2bcd 0         ab2d2 abc3  ab2d2 a2bd2 0         abc2d abc2d abc3  a2|
| 0     0     abcd      0     0     0     0     abd2      0     0     0     0 |
| abc2  a2c2  ab2c+a2bd abcd  abcd  abcd  a2cd  a2c2+ab2d abd2  abd2  abcd  a2|
| -a2bc -a3c  -a2b2     -a2bd -ab2c -a2bd -a3d  -a3c      -ab2d -ab2d -ab2c -a|
|                                                                             |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -ab3d -a2b2d 0 0 0 -ab2cd 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ab3c  a2b2c  0 0 0 ab2c2  0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ab4   a2b3   0 0 0 ab3c   0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a2b3 -a3b2  0 0 0 -a2b2c 0 0 0 0 0 0 0 0 0 |
|-----------------------------------------------------------------------------|
|a4c3 a3c4-a2b2c2d a2c5-a2bc2d2 a2bc2d-a3cd2 a2b3cd-a4c2d a3c3d-a2b2cd2 a2c4d-|
|                                                                             |
|                                                                             |
|d -ab3d2 -ab2c2d -ab3c2 -a2bc3 -ab2c2d -abc4  -ab3cd -a2bc2d -ab2cd2 -abc3d -|
|  0      0       abc3   abc2d  0       0      abc2d  abcd2   0       0      a|
|  -ab2cd -ab2d2  a2bc2  ab2c2  -abc3   -abc2d a2bcd  ab2cd   -abc2d  -abcd2 a|
|  a2b2d  ab3d    0      0      a2bc2   ab2c2  0      0       a2bcd   ab2cd  0|
|                                                                             |
|3   ac3d  ac2d2  acd3   ad4   b4d  b3cd  b3d2  b2c2d b2cd2  b2d3   bc3d  bc2d|
|cd2 -ac4  -ac3d  -ac2d2 -acd3 -b4c -b3c2 -b3cd -b2c3 -b2c2d -b2cd2 -bc4  -bc3|
|2d2 -abc3 -abc2d -abcd2 -abd3 -b5  -b4c  -b4d  -b3c2 -b3cd  -b3d2  -b2c3 -b2c|
|d2  a2c3  a2c2d  a2cd2  a2d3  ab4  ab3c  ab3d  ab2c2 ab2cd  ab2d2  abc3  abc2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|--- cokernel {3} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
||            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 |
||            {3} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
||            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 |
||            {3} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
||            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 |
||            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d |
||            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
||            {3} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 |
||            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
||            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
||            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
||                                                                            |
|                                                                             |
|0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2|
|0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0 |
|0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0 |
|ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-ad2 b3d-a2cd ac2d-b2d2 c3d-bd3 a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3 b2c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0 |
|   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0 |
|   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0 |
|d2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bc|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   c2d |
| 0   0   0   0   0   0   bd2 bcd b2d abd 0   0   0   0   0   0   0   0   0   |
| b2c abc 0   0   0   0   0   0   0   0   bd2 bcd b2d abd 0   0   0   0   0   |
| 0   0   bcd bc2 b2c abc 0   0   0   0   0   0   0   0   bd2 bcd b2d abd 0   |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2d3 bc3-ac2d b3c2-a2c3 ac4-b2c2d c5-bc2d2 bc2d-acd2 b3cd-a2c2d ac3d-b2cd2 c4d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|   bcd2 0       bd3  c3d  c3d  0 bd3  0 acd2 acd2 acd2 c2d2 c2d2 0 0 0       |
|   0    cd2     0    0    0    0 0    0 -d3  -d3  -d3  0    0    0 0 -a2cd   |
|d  c2d  bcd+ad2 cd2  cd2  cd2  0 cd2  0 -bd2 -bd2 -bd2 d3   d3   0 0 -a2bc-a3|
|c2 -acd -abd    -ad2 -bcd -bcd 0 -ad2 0 0    0    0    -bd2 -bd2 0 0 a3b     |
|                                                                             |
| 0 0 0 0 -c3d -bc2d -ac2d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
| 0 0 0 0 c4   bc3   ac3   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
| 0 0 0 0 bc3  b2c2  abc2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
| 0 0 0 0 -ac3 -abc2 -a2c2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                                                                             |
|c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 bd3 c4 c3d c2d2 cd3 d4 |) <----- 0 : {-3, |
|                                                                0            |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|a2b2c2-ab4d ab2c3-ab3d2 ab2c2-a2bcd ab4c-a3bc2 a2bc3-ab3cd abc4-ab2cd2 ab2cd-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|c3  0         0          abc2d a2c2d 0         abcd2 abcd2 ac4   abcd2 0     |
|    ac3       0          0     0     ac2d      0     0     0     0     acd2  |
|cd  a2c2+ab2d ac3-abd2   abd2  a2d2  abc2+a2cd ac2d  ac2d  ac2d  ac2d  abcd+a|
|2bc -ab3      -a2c2+ab2d -ab2d -a2bd -a2bc     -a2cd -a2cd -abc2 -a2cd -a2bd |
|                                                                             |
|0 0 0 0 0 0 0 0 -abc2d -ab2cd -a2bcd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|0 0 0 0 0 0 0 0 abc3   ab2c2  a2bc2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|0 0 0 0 0 0 0 0 ab2c2  ab3c   a2b2c  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|0 0 0 0 0 0 0 0 -a2bc2 -a2b2c -a3bc  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|-----------------------------------------------------------------------------|
|a2bcd3 a2bcd2-a3d3 a2b3d2-a4cd2 a3c2d2-a2b2d3 a2c3d2-a2bd4 ab4c-a2b3d ab6-a3b|
|                                                                             |
|                                                                             |
|ab3d2 -a2bcd2 -ab2d3 -abc2d2 -ab2c3 -a2c4 -abc3d -ac5  -ab2c2d -a2c3d -abc2d2|
|bcd2  abd3    0      0       ac4    ac3d  0      0     ac3d    ac2d2  0      |
|2bd2  ab2d2   -abcd2 -abd3   a2c3   abc3  -ac4   -ac3d a2c2d   abc2d  -ac3d  |
|      0       a2bd2  ab2d2   0      0     a2c3   abc3  0       0      a2c2d  |
|                                                                             |
|2  bcd3   bd4   c4d  c3d2  c2d3   cd4   d5   0 0 0 0 |) <----- 0 : {-5, 7}   |
|d  -bc2d2 -bcd3 -c5  -c4d  -c3d2  -c2d3 -cd4 0 0 0 0 |     0                 |
|2d -b2cd2 -b2d3 -bc4 -bc3d -bc2d2 -bcd3 -bd4 0 0 0 0 |                       |
|d  abcd2  abd3  ac4  ac3d  ac2d2  acd3  ad4  0 0 0 0 |                       |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | : {-1, 2}                            |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                                      |
|0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 |                                      |
|0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 |                                      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a |                                      |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0  0  0  |) <----- 0 : {-1, 3}                                              |
| d2 0  0  |     0                                                            |
| 0  d2 0  |                                                                  |
| 0  0  d2 |                                                                  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| b2d bc2 bcd bd2 c3 c2d cd2 d3 |) <------------------------------- cokernel {|
|                                     {2} | 1 0 0 0 0 0 0 0 0 0 |            {|
|                                     {2} | 0 1 0 0 0 0 0 0 0 0 |            {|
|                                     {2} | 0 0 1 0 0 0 0 0 0 0 |            {|
|                                     {2} | 0 0 0 1 0 0 0 0 0 0 |            {|
|                                     {2} | 0 0 0 0 1 0 0 0 0 0 |            {|
|                                     {2} | 0 0 0 0 0 1 0 0 0 0 |            {|
|                                     {2} | 0 0 0 0 0 0 1 0 0 0 |            {|
|                                     {2} | 0 0 0 0 0 0 0 1 0 0 |            {|
|                                     {2} | 0 0 0 0 0 0 0 0 1 0 |            {|
|                                     {2} | 0 0 0 0 0 0 0 0 0 1 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {4} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {4} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {4} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {4} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {4} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {4} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {4} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {4} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {4} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {4} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {4} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {4} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                     {3} | 0 0 0 0 0 0 0 0 0 0 |             |
|                                                                             |
|  bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0   0   d3 0  0  0  |, |
|  0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0   0   0  d3 0  0  |  |
|  0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2 0   0  0  d3 0  |  |
|d 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0   cd2 0  0  0  d3 |  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|c3 bc2 ac2 0   0  0   0   0   0  0   0   0   0  0   0   0   0   0   0   0   0|
|0  0   0   c2d c3 bc2 ac2 0   0  0   0   0   0  0   0   cd2 c2d bcd acd 0   0|
|0  0   0   0   0  0   0   c2d c3 bc2 ac2 0   0  0   0   0   0   0   0   cd2 c|
|0  0   0   0   0  0   0   0   0  0   0   c2d c3 bc2 ac2 0   0   0   0   0   0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-bcd3 bcd2-ad3 b3d2-a2cd2 ac2d2-b2d3 c3d2-bd4 a4 a3b a3c a3d a2b2 a2bc a2bd a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|  0         0 0 0 0 0 0 0 0 0 0 0 0 0 0          0 0          0          0 0 |
|  -a2cd     0 0 0 0 0 0 0 0 0 0 0 0 0 -a2c2+ab2d 0 -abcd      -abcd      0 0 |
|d -a2bc-a3d 0 0 0 0 0 0 0 0 0 0 0 0 0 ab3-a3c    0 -ab2c-a2bd -ab2c-a2bd 0 0 |
|  a3b       0 0 0 0 0 0 0 0 0 0 0 0 0 0          0 a2b2       a2b2       0 0 |
|                                                                             |
| 0 0 0 0 0 a2d  abd  acd  ad2  b2d  bcd  bd2  c2d  cd2  d3   a4 0  0  0  a3b |
| 0 0 0 0 0 -a2c -abc -ac2 -acd -b2c -bc2 -bcd -c3  -c2d -cd2 0  a4 0  0  0   |
| 0 0 0 0 0 -a2b -ab2 -abc -abd -b3  -b2c -b2d -bc2 -bcd -bd2 0  0  a4 0  0   |
| 0 0 0 0 0 a3   a2b  a2c  a2d  ab2  abc  abd  ac2  acd  ad2  0  0  0  a4 0   |
|                                                                             |
|6}                                                                           |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|a2bd2 ab4d-a3bcd a2bc2d-ab3d2 abc3d-ab2d3 abc3-a2c2d ab3c2-a3c3 a2c4-ab2c2d a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|    abd3  ac3d  ac3d  abd3  0 a2cd2 a2cd2 a2cd2 ac2d2 ac2d2 ab4   ab3c  b5   |
|    0     0     0     0     0 -ad3  -ad3  -ad3  0     0     -ab2c -abc2 -b3c |
|2d2 acd2  acd2  acd2  acd2  0 -abd2 -abd2 -abd2 ad3   ad3   -a2b2 -a2bc -ab3 |
|    -a2d2 -abcd -abcd -a2d2 0 0     0     0     -abd2 -abd2 0     0     0    |
|                                                                             |
|0 0 0 0 -ac3d -abc2d -a2c2d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 ac4   abc3   a2c3   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 abc3  ab2c2  a2bc2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 -a2c3 -a2bc2 -a3c2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|-----------------------------------------------------------------------------|
|3c a2b3c2-ab5d ab3c3-ab4d2 ab3c2-a2b2cd ab5c-a3b2c2 a2b2c3-ab4cd ab2c4-ab3cd2|
|                                                                             |
|                                                                             |
| -ac4d  -ab2cd2 -a2c2d2 -abcd3 -ac3d2 -ab2d3 -a2cd3 -abd4 -ac2d3 -b6 -ab4c -b|
| 0      ac2d2   acd3    0      0      acd3   ad4    0     0      b4c b4d   0 |
| -ac2d2 a2cd2   abcd2   -ac2d2 -acd3  a2d3   abd3   -acd3 -ad4   ab4 b5    -b|
| abc2d  0       0       a2cd2  abcd2  0      0      a2d3  abd3   0   0     ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|2} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|2} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|2} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 |
|2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 |
|2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 |
|2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a |
|2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|{2} | -ab2 -a2c -abd -ac2 -b3 -abc -b2d -bc2 -b2c -ac2 -bcd -c3 -b2d -acd -bd|
|{3} | ac   ad   0    0    bc  bd   0    0    c2   cd   0    0   cd   d2   0  |
|{3} | a2   ab   -ac  -ad  ab  b2   -bc  -bd  ac   bc   -c2  -cd ad   bd   -cd|
|{3} | 0    0    a2   ab   0   0    ab   b2   0    0    ac   bc  0    0    ad |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|   0   0   0   0   0   0   0  0   0   0   0  0   0   0   0  0   0   0   ad  b|
|   0   0   0   0   0   0   d3 cd2 bd2 ad2 0  0   0   0   0  0   0   0   -ac -|
|2d bcd acd 0   0   0   0   0  0   0   0   d3 cd2 bd2 ad2 0  0   0   0   -ab -|
|   0   0   cd2 c2d bcd acd 0  0   0   0   0  0   0   0   d3 cd2 bd2 ad2 a2  a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2c2 a2cd a2d2 ab3 ab2c ab2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0 0 0 0 0         0 0 0 0 0 0 0 0 0 0         0          0         0         |
|0 0 0 0 -ac3+abd2 0 0 0 0 0 0 0 0 0 -abc2+b3d -a2c2+ab2d -ac3+abd2 -ac3+b2cd+|
|0 0 0 0 0         0 0 0 0 0 0 0 0 0 b4-a2bc   ab3-a3c    0         b3c+ab2d  |
|0 0 0 0 ab3-a3c   0 0 0 0 0 0 0 0 0 0         0          ab3-a3c   -a3c      |
|                                                                             |
|0   0   0   a3c 0   0   0   a3d 0   0   0   a2b2 0    0    0    a2bc 0    0  |
|a3b 0   0   0   a3c 0   0   0   a3d 0   0   0    a2b2 0    0    0    a2bc 0  |
|0   a3b 0   0   0   a3c 0   0   0   a3d 0   0    0    a2b2 0    0    0    a2b|
|0   0   a3b 0   0   0   a3c 0   0   0   a3d 0    0    0    a2b2 0    0    0  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|c5-abc2d2 abc2d-a2cd2 ab3cd-a3c2d a2c3d-ab2cd2 ac4d-abcd3 abcd2-a2d3 ab3d2-a3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|b4d  b4d  ab3d  0         b3c2 b3c2 ab2c2 b4c   b4c   b3cd  b3cd  b3cd  ab2cd|
|0    0    0     -abc2+b3d 0    0    0     -b2c2 -b2c2 0     0     0     0    |
|b3c  b3c  ab2c  b4-a2bc   b3d  b3d  ab2d  -ab2c -ab2c b2c2  b2c2  b2c2  abc2 |
|-ab3 -ab3 -a2b2 0         -b4  -b4  -ab3  0     0     -ab2c -ab2c -ab2c -a2bc|
|                                                                             |
| 0 0 0 0 0 0 0 0 -b4d -ab3d 0 0 0 -b3cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -b2|
| 0 0 0 0 0 0 0 0 b4c  ab3c  0 0 0 b3c2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b2c|
| 0 0 0 0 0 0 0 0 b5   ab4   0 0 0 b4c   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b3c|
| 0 0 0 0 0 0 0 0 -ab4 -a2b3 0 0 0 -ab3c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -ab|
|-----------------------------------------------------------------------------|
| ab3cd-a2b2d2 ab5d-a3b2cd a2b2c2d-ab4d2 ab2c3d-ab3d3 ab2c3-a2bc2d ab4c2-a3bc3|
|                                                                             |
|                                                                             |
|5d -b4c2 -b5c -ab3c2 -b4cd -b3c3 -b5d -ab3cd -b4d2 -b3c2d -b4c2 -ab2c3 -b3c2d|
|   0     b3c2 b3cd   0     0     b3cd b3d2   0     0      b2c3  b2c2d  0     |
|4c -b4d  ab3c b4c    -b3c2 -b3cd ab3d b4d    -b3cd -b3d2  ab2c2 b3c2   -b2c3 |
|4  b5    0    0      ab3c  b4c   0    0      ab3d  b4d    0     0      ab2c2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0 0 0 0 | : {-2, 2}                                                          |
|0 0 0 0 |                                                                    |
|0 0 0 0 |                                                                    |
|0 0 0 0 |                                                                    |
|0 0 0 0 |                                                                    |
|0 0 0 0 |                                                                    |
|0 0 0 0 |                                                                    |
|0 0 0 0 |                                                                    |
|0 0 0 0 |                                                                    |
|d c b a |                                                                    |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2 -c2d a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0 |
|  0    0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0 |
|  -d2  0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab|
|  bd   0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|d  cd  d2  a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0 |
|bc -c2 -cd 0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab|
|b2 -bc -bd 0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0 |
|b  ac  ad  0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|b2cd b2d2 bc3 bc2d bcd2 bd3 c4 c3d c2d2 cd3 d4 |, | a2bc-a3d a2b3-a4c a3c2-a2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|     0 0 0 0 0 0         0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a2b2 -a3c -a2bd -a2c2 -|
|abd2 0 0 0 0 0 -bc3+ac2d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a2c   a2d  0     0     a|
|     0 0 0 0 0 -b3d+a2cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a3    a2b  -a2c  -a2d  a|
|     0 0 0 0 0 b4-a2bc   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0     0    a3    a2b   0|
|                                                                             |
|  0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    |
|  0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 |
|c 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    |
|  a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|cd2 a2c2d2-ab2d3 ac3d2-abd4 b4c-ab3d b6-a2b3c ab3c2-b5d b3c3-b4d2 b3c2-ab2cd |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0        b3d2  b2c3 b3d2  ab2d2 0        b2c2d b2c2d b2c3 abc3  0        0  |
| b2cd     0     0    0     0     b2d2     0     0     0    0     bc3      0  |
| b3c+ab2d b2cd  b2cd b2cd  abcd  abc2+b3d b2d2  b2d2  b2cd abcd  abc2+b3d bc3|
| -ab3     -ab2d -b3c -ab2d -a2bd -a2bc    -b3d  -b3d  -b3c -ab2c -b4      -ab|
|                                                                             |
|c2d -b3cd -ab2cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -bc3d -b2c2d|
|3   b3c2  ab2c2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 bc4   b2c3  |
|2   b4c   ab3c   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b2c3  b3c2  |
|2c2 -ab3c -a2b2c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -abc3 -ab2c2|
|-----------------------------------------------------------------------------|
| a2bc4-ab3c2d abc5-ab2c2d2 ab2c2d-a2bcd2 ab4cd-a3bc2d a2bc3d-ab3cd2 abc4d-ab2|
|                                                                             |
|                                                                             |
| -b2c4  -b4cd -ab2c2d -b3cd2 -b2c3d -b4d2 -ab2cd2 -b3d3  -b2c2d2 -b3c3 -abc4 |
| 0      b2c2d b2cd2   0      0      b2cd2 b2d3    0      0       bc4   bc3d  |
| -b2c2d ab2cd b3cd    -b2c2d -b2cd2 ab2d2 b3d2    -b2cd2 -b2d3   abc3  b2c3  |
| b3c2   0     0       ab2cd  b3cd   0     0       ab2d2  b3d2    0     0     |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|  0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0  |
|  0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2|
|2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0  |
|  ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|  0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2|
|2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0  |
|  ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0  |
|  0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|b2d a2c3-a2bd2 ab2c-a2bd ab4-a3bc a2bc2-ab3d abc3-ab2d2 abc2-a2cd ab3c-a3c2 a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|ab3 -a2bc -ab2d -abc2 -ab2c -a2c2 -abcd -ac3 -ab2d -a2cd -abd2 -ac2d -b4 -ab2|
|bc  abd   0     0     ac2   acd   0     0    acd   ad2   0     0     b2c b2d |
|2b  ab2   -abc  -abd  a2c   abc   -ac2  -acd a2d   abd   -acd  -ad2  ab2 b3  |
|    0     a2b   ab2   0     0     a2c   abc  0     0     a2d   abd   0   0   |
|                                                                             |
|0    0    ab3 0   0   0   ab2c 0    0    0    ab2d 0    0    0    abc2 0    0|
|0    0    0   ab3 0   0   0    ab2c 0    0    0    ab2d 0    0    0    abc2 0|
|a2d2 0    0   0   ab3 0   0    0    ab2c 0    0    0    ab2d 0    0    0    a|
|0    a2d2 0   0   0   ab3 0    0    0    ab2c 0    0    0    ab2d 0    0    0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|b5c-a2b2c2 ab2c3-b4cd b2c4-b3cd2 b3cd-ab2d2 b5d-a2b2cd ab2c2d-b4d2 b2c3d-b3d3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|       b2c2d abc2d 0         b2cd2 b2cd2 bc4   b2cd2 abcd2 0         b2d3  bc|
|       0     0     bc2d      0     0     0     0     0     bcd2      0     0 |
|-b2d2  b2d2  abd2  b2c2+abcd bc2d  bc2d  bc2d  bc2d  ac2d  b2cd+abd2 bcd2  bc|
|c2+b3d -b3d  -ab2d -ab2c     -abcd -abcd -b2c2 -abcd -a2cd -ab2d     -abd2 -b|
|                                                                             |
| -abc2d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -c4|
| abc3   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c5 |
| ab2c2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 bc4|
| -a2bc2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -ac|
|-----------------------------------------------------------------------------|
|cd3 ab2cd2-a2bd3 ab4d2-a3bcd2 a2bc2d2-ab3d3 abc3d2-ab2d4 abc4-a2c3d ab3c3-a3c|
|                                                                             |
|                                                                             |
|-b2c3d -bc5  -b3c2d -abc3d -b2c2d2 -bc4d  -b3cd2 -abc2d2 -b2cd3 -bc3d2 -b3d3 |
|0      0     bc3d   bc2d2  0       0      bc2d2  bcd3    0      0      bcd3  |
|-bc4   -bc3d abc2d  b2c2d  -bc3d   -bc2d2 abcd2  b2cd2   -bc2d2 -bcd3  abd3  |
|abc3   b2c3  0      0      abc2d   b2c2d  0      0       abcd2  b2cd2  0     |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   |
| 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd |
| ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   |
| 0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd |
| ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   |
| 0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   |
| 0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2c3-ab2cd ac4-abcd2 abcd-a2d2 ab3d-a3cd a2c2d-ab2d2 ac3d-abd3 b3c-ab2d b5-a2b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|c -b3d -b2c2 -b3c -abc2 -b2cd -bc3 -b3d -abcd -b2d2 -bc2d -b2c2 -ac3 -bc2d -c|
|  0    0     bc2  bcd   0     0    bcd  bd2   0     0     c3    c2d  0     0 |
|  -b2c -b2d  abc  b2c   -bc2  -bcd abd  b2d   -bcd  -bd2  ac2   bc2  -c3   -c|
|  ab2  b3    0    0     abc   b2c  0    0     abd   b2d   0     0    ac2   bc|
|                                                                             |
|    0    abcd 0    0    0    abd2 0    0    0    ac3 0   0   0   ac2d 0    0 |
|    0    0    abcd 0    0    0    abd2 0    0    0   ac3 0   0   0    ac2d 0 |
|bc2 0    0    0    abcd 0    0    0    abd2 0    0   0   ac3 0   0    0    ac|
|    abc2 0    0    0    abcd 0    0    0    abd2 0   0   0   ac3 0    0    0 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| b2c3-abc2d b4c2-a2bc3 abc4-b3c2d bc5-b2c2d2 b2c2d-abcd2 b4cd-a2bc2d abc3d-b3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|3d  bc3d  b2d3  abd3  0         bc2d2 bc2d2 c5             bc4   ac4   0     |
|    0     0     0     bd3       0     0     0              0     0     c4    |
|d2  bcd2  bcd2  acd2  ac2d+b2d2 bd3   bd3   bd3            bc2d  ac2d  b2cd+a|
|2cd -b2cd -abd2 -a2d2 -a2cd     -b2d2 -b2d2 -bc3+ac2d-b2d2 -b2c2 -abc2 -b3c+a|
|                                                                             |
|d -bc3d -ac3d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|  bc4   ac4   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|  b2c3  abc3  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|4 -abc3 -a2c3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|-----------------------------------------------------------------------------|
|4 a2c5-ab2c3d ac6-abc3d2 abc3d-a2c2d2 ab3c2d-a3c3d a2c4d-ab2c2d2 ac5d-abc2d3 |
|                                                                             |
|                                                                             |
|-abcd3 -b2d4 -bc2d3 -b2c4 -ac5 -bc4d -c6  -b2c3d -ac4d -bc3d2 -c5d  -b2c2d2 -|
|bd4    0     0      c5    c4d  0     0    c4d    c3d2  0      0     c3d2    c|
|b2d3   -bcd3 -bd4   ac4   bc4  -c5   -c4d ac3d   bc3d  -c4d   -c3d2 ac2d2   b|
|0      abd3  b2d3   0     0    ac4   bc4  0      0     ac3d   bc3d  0       0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0   0   d3 0  0  |
|0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0   0   0  d3 0  |
|bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2 0   0  0  d3 |
|0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0   cd2 0  0  0  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0   0   d3 0 |
|bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0   0   0  d3|
|0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2 0   0  0 |
|0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0   cd2 0  0 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2c ab2c2-b4d b2c3-b3d2 b2c2-abcd b4c-a2bc2 abc3-b3cd bc4-b2cd2 b2cd-abd2 b4d-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|4  -b2cd -ac2d -bcd2 -c3d -b2d2 -acd2 -bd3 -c2d2 a4 0  0  0  a3b 0   0   0   |
|   c2d   cd2   0     0    cd2   d3    0    0     0  a4 0  0  0   a3b 0   0   |
|2d acd   bcd   -c2d  -cd2 ad2   bd2   -cd2 -d3   0  0  a4 0  0   0   a3b 0   |
|2  0     0     acd   bcd  0     0     ad2  bd2   0  0  0  a4 0   0   0   a3b |
|                                                                             |
|   0    acd2 0    0    0    ad3 0   0   0   b4 0  0  0  b3c 0   0   0   b3d 0|
|   0    0    acd2 0    0    0   ad3 0   0   0  b4 0  0  0   b3c 0   0   0   b|
|2d 0    0    0    acd2 0    0   0   ad3 0   0  0  b4 0  0   0   b3c 0   0   0|
|   ac2d 0    0    0    acd2 0   0   0   ad3 0  0  0  b4 0   0   0   b3c 0   0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|cd2 bc4d-b2cd3 b2cd2-abd3 b4d2-a2bcd2 abc2d2-b3d3 bc3d2-b2d4 bc4-ac3d b3c3-a2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|         0         bc3d  ac3d  0         0          bc2d2 ac2d2 0         bcd|
|         0         0     0     c3d       0          0     0     c2d2      0  |
|bd2      c4-bcd2   bcd2  acd2  ac2d+b2d2 c3d-bd3    bd3   ad3   bc2d+acd2 c2d|
|2c2-ab2d -ac3+b2cd -b2cd -abcd -b3d      -ac2d+b2d2 -b2d2 -abd2 -abcd     -ac|
|                                                                             |
| 0 0 0 0 0 0 0 0 a3d  a2bd  a2cd  a2d2  ab2d  abcd  abd2  ac2d  acd2  ad3   b|
| 0 0 0 0 0 0 0 0 -a3c -a2bc -a2c2 -a2cd -ab2c -abc2 -abcd -ac3  -ac2d -acd2 -|
| 0 0 0 0 0 0 0 0 -a3b -a2b2 -a2bc -a2bd -ab3  -ab2c -ab2d -abc2 -abcd -abd2 -|
| 0 0 0 0 0 0 0 0 a4   a3b   a3c   a3d   a2b2  a2bc  a2bd  a2c2  a2cd  a2d2  a|
|-----------------------------------------------------------------------------|
|abc2d2-a2cd3 ab3cd2-a3c2d2 a2c3d2-ab2cd3 ac4d2-abcd4 abcd3-a2d4 ab3d3-a3cd3 a|
|                                                                             |
|                                                                             |
|ac3d2 -bc2d3 -c4d2 -b2cd3 -ac2d3 -bcd4 -c3d3 -b2d4 -acd4 -bd5 -c2d4 0 0 0 0 ||
|2d3   0      0     c2d3   cd4    0     0     cd4   d5    0    0     0 0 0 0 ||
|c2d2  -c3d2  -c2d3 acd3   bcd3   -c2d3 -cd4  ad4   bd4   -cd4 -d5   0 0 0 0 ||
|      ac2d2  bc2d2 0      0      acd3  bcd3  0     0     ad4  bd4   0 0 0 0 ||
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0  |) <------------------------------------------------------------------- co|
|0  |     {4} | 1 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|0  |     {5} | 0 1 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|d3 |     {5} | 0 0 0 0 0 -1 0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 -1 0 0 0 0  0 0 0 0  0 0 |     |
|         {4} | 0 0 1 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 1 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 -1 0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 -1 0 0 0 0  0 0 |     |
|         {4} | 0 0 0 0 1 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  1 0 0 0  0 0 0 0  0 0 |     |
|         {4} | 0 0 0 0 0 0  1 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  1 0 0 0  0 0 |     |
|         {4} | 0 0 0 0 0 0  0 1 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 1 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 -1 0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 -1 0 0 |     |
|         {4} | 0 0 0 0 0 0  0 0 0 1 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {4} | 0 0 0 0 0 0  0 0 0 0 0  1 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  1 0 |     |
|         {4} | 0 0 0 0 0 0  0 0 0 0 0  0 0  1 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 1 0 0  0 0 0 0  0 0 |     |
|         {4} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 1 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 1 0 0  0 0 |     |
|         {4} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 1 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 1 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|         {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |     |
|                                                                             |
| 0  0  |, {4} | ad  bd  cd  d2  a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a|
| 0  0  |  {4} | -ac -bc -c2 -cd 0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0|
| d3 0  |  {4} | -ab -b2 -bc -bd 0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0|
| 0  d3 |  {4} | a2  ab  ac  ad  0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|a2bcd abc2d-b3d2 bc3d-b2d3 bc3-ac2d b3c2-a2c3 ac4-b2c2d c5-bc2d2 bc2d-acd2 b3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|a3c 0   0   0   a3d 0   0   0   a2b2 0    0    0    a2bc 0    0    0    a2bd |
|0   a3c 0   0   0   a3d 0   0   0    a2b2 0    0    0    a2bc 0    0    0    |
|0   0   a3c 0   0   0   a3d 0   0    0    a2b2 0    0    0    a2bc 0    0    |
|0   0   0   a3c 0   0   0   a3d 0    0    0    a2b2 0    0    0    a2bc 0    |
|                                                                             |
|   0   0   b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0    bc3 0 |
|3d 0   0   0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0   bc|
|   b3d 0   0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0   0 |
|   0   b3d 0    0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0   0 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|c4 ac5-b2c3d c6-bc3d2 bc3d-ac2d2 b3c2d-a2c3d ac4d-b2c2d2 c5d-bc2d3 bc2d2-acd3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|3  bcd3  c4d   c4d   bcd3  0        bd4  c3d2  c3d2  0 bd4  0 acd3 acd3 acd3 |
|   0     0     0     0     cd3      0    0     0     0 0    0 -d4  -d4  -d4  |
|2  c2d2  c2d2  c2d2  c2d2  bcd2+ad3 cd3  cd3   cd3   0 cd3  0 -bd3 -bd3 -bd3 |
|d2 -acd2 -bc2d -bc2d -acd2 -abd2    -ad3 -bcd2 -bcd2 0 -ad3 0 0    0    0    |
|                                                                             |
|3d  b2cd  b2d2  bc2d  bcd2  bd3   c3d  c2d2  cd3   d4   0 0 0 0 |, {4} | a3d |
|b3c -b2c2 -b2cd -bc3  -bc2d -bcd2 -c4  -c3d  -c2d2 -cd3 0 0 0 0 |  {4} | -a3c|
|b4  -b3c  -b3d  -b2c2 -b2cd -b2d2 -bc3 -bc2d -bcd2 -bd3 0 0 0 0 |  {4} | -a3b|
|b3  ab2c  ab2d  abc2  abcd  abd2  ac3  ac2d  acd2  ad3  0 0 0 0 |  {4} | a4  |
|-----------------------------------------------------------------------------|
|2c2d3-ab2d4 ac3d3-abd5 b5c-ab4d b7-a2b4c ab4c2-b6d b4c3-b5d2 b4c2-ab3cd b6c-a|
|                                                                             |
|                                                                             |
|, {2} | -a4b2 -a5c -a4bd -a4c2 -a3b3 -a4bc -a3b2d -a3bc2 -a3b2c -a4c2 -a3bcd |
|  {3} | a4c   a4d  0     0     a3bc  a3bd  0      0      a3c2   a3cd  0      |
|  {3} | a5    a4b  -a4c  -a4d  a4b   a3b2  -a3bc  -a3bd  a4c    a3bc  -a3c2  |
|  {3} | 0     0    a5    a4b   0     0     a4b    a3b2   0      0     a4c    |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|kernel {4} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {4} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {4} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {4} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|       {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0 |
|   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0 |
|   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0 |
|   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|cd-a2c2d ac3d-b2cd2 c4d-bcd3 bcd2-ad3 b3d2-a2cd2 ac2d2-b2d3 c3d2-bd4 a4 a3b a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0    0    ab|
|a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0    0 |
|0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0 |
|0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0 |
|                                                                             |
|  0   0   bc2d 0    0    0    bcd2 0    0    0    bd3 0   0   0   c4 0  0  0 |
|3 0   0   0    bc2d 0    0    0    bcd2 0    0    0   bd3 0   0   0  c4 0  0 |
|  bc3 0   0    0    bc2d 0    0    0    bcd2 0    0   0   bd3 0   0  0  c4 0 |
|  0   bc3 0    0    0    bc2d 0    0    0    bcd2 0   0   0   bd3 0  0  0  c4|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| b3cd2-a2c2d2 ac3d2-b2cd3 c4d2-bcd4 bcd3-ad4 b3d3-a2cd3 ac2d3-b2d4 c3d3-bd5 0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|c2d3 c2d3 0 0 0         0         0 0 0 0 0 0 0 0 0 0 0 0 0 0           0 0  |
|0    0    0 0 -a3cd     -a3cd     0 0 0 0 0 0 0 0 0 0 0 0 0 -a3c2+a2b2d 0 -a2|
|d4   d4   0 0 -a3bc-a4d -a3bc-a4d 0 0 0 0 0 0 0 0 0 0 0 0 0 a2b3-a4c    0 -a2|
|-bd3 -bd3 0 0 a4b       a4b       0 0 0 0 0 0 0 0 0 0 0 0 0 0           0 a3b|
|                                                                             |
| a2bd  a2cd  a2d2  ab2d  abcd  abd2  ac2d  acd2  ad3   b3d  b2cd  b2d2  bc2d |
| -a2bc -a2c2 -a2cd -ab2c -abc2 -abcd -ac3  -ac2d -acd2 -b3c -b2c2 -b2cd -bc3 |
| -a2b2 -a2bc -a2bd -ab3  -ab2c -ab2d -abc2 -abcd -abd2 -b4  -b3c  -b3d  -b2c2|
| a3b   a3c   a3d   a2b2  a2bc  a2bd  a2c2  a2cd  a2d2  ab3  ab2c  ab2d  abc2 |
|-----------------------------------------------------------------------------|
|2b3c2 ab3c3-b5cd b3c4-b4cd2 b4cd-ab3d2 b6d-a2b3cd ab3c2d-b5d2 b3c3d-b4d3 b3c3|
|                                                                             |
|                                                                             |
|-a3c3 -a3b2d -a4cd -a3bd2 -a3c2d -a2b4 -a3b2c -a2b3d -a2b2c2 -a2b3c -a3bc2 -a|
|0     a3cd   a3d2  0      0      a2b2c a2b2d  0      0       a2bc2  a2bcd  0 |
|-a3cd a4d    a3bd  -a3cd  -a3d2  a3b2  a2b3   -a2b2c -a2b2d  a3bc   a2b2c  -a|
|a3bc  0      0     a4d    a3bd   0     0      a3b2   a2b3    0      0      a3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|  acd 0   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0  |
|  0   acd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0  |
|  0   0   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0  |
|2 0   0   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab2d abc2 abcd abd2 ac3 ac2d ac|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|3 0   0   0   ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abc|
|  ab3 0   0   0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0  |
|  0   ab3 0   0    0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0  |
|  0   0   ab3 0    0    0    ab2c 0    0    0    ab2d 0    0    0    abc2 0  |
|                                                                             |
| c3d 0   0   0   c2d2 0    0    0    cd3 0   0   0   d4 0  0  0  |, {4} | a2d|
| 0   c3d 0   0   0    c2d2 0    0    0   cd3 0   0   0  d4 0  0  |  {4} | -a2|
| 0   0   c3d 0   0    0    c2d2 0    0   0   cd3 0   0  0  d4 0  |  {4} | -a2|
| 0   0   0   c3d 0    0    0    c2d2 0   0   0   cd3 0  0  0  d4 |  {4} | a3 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| |, | a3bc-a4d a3b3-a5c a4c2-a3b2d a3c3-a3bd2 a2b2c-a3bd a2b4-a4bc a3bc2-a2b3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|         0           0 0 0 0 0 0 0           0 0 0 0 0 0 0 0 0 0           0 |
|bcd      -a2bcd      0 0 0 0 0 0 -a2c3+a2bd2 0 0 0 0 0 0 0 0 0 -a2bc2+ab3d -a|
|b2c-a3bd -a2b2c-a3bd 0 0 0 0 0 0 0           0 0 0 0 0 0 0 0 0 ab4-a3bc    a2|
|2        a3b2        0 0 0 0 0 0 a2b3-a4c    0 0 0 0 0 0 0 0 0 0           0 |
|                                                                             |
| bcd2  bd3   c3d  c2d2  cd3   d4   0 0 0 0 |) <----- 0 : {-4, 6}             |
| -bc2d -bcd2 -c4  -c3d  -c2d2 -cd3 0 0 0 0 |     0                           |
| -b2cd -b2d2 -bc3 -bc2d -bcd2 -bd3 0 0 0 0 |                                 |
| abcd  abd2  ac3  ac2d  acd2  ad3  0 0 0 0 |                                 |
|-----------------------------------------------------------------------------|
|-ab2c2d b5c2-a2b2c3 ab2c4-b4c2d b2c5-b3c2d2 b3c2d-ab2cd2 b5cd-a2b2c2d ab2c3d-|
|                                                                             |
|                                                                             |
|2b2cd -a2bc3 -a2b3d -a3bcd -a2b2d2 -a2bc2d -a2b2c2 -a3c3 -a2bc2d -a2c4  -a2b2|
|      0      a2bcd  a2bd2  0       0       a2c3    a2c2d 0       0      a2c2d|
|2bc2  -a2bcd a3bd   a2b2d  -a2bcd  -a2bd2  a3c2    a2bc2 -a2c3   -a2c2d a3cd |
|bc    a2b2c  0      0      a3bd    a2b2d   0       0     a3c2    a2bc2  0    |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | : {-2, 3}       |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 |                 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a |                 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| bc2 0   0   0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   |
| 0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   |
| 0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   |
| 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|d2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 bd3 c4 c3d c2d2 cd3 d4 |) <---|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                            {|
|                                                                             |
|d 0    0    0    abd2 0    0    0    ac3 0   0   0   ac2d 0    0    0    acd2|
|  abcd 0    0    0    abd2 0    0    0   ac3 0   0   0    ac2d 0    0    0   |
|  0    abcd 0    0    0    abd2 0    0   0   ac3 0   0    0    ac2d 0    0   |
|  0    0    abcd 0    0    0    abd2 0   0   0   ac3 0    0    0    ac2d 0   |
|                                                                             |
|  abd  acd  ad2  b2d  bcd  bd2  c2d  cd2  d3   a4 0  0  0  a3b 0   0   0   a3|
|c -abc -ac2 -acd -b2c -bc2 -bcd -c3  -c2d -cd2 0  a4 0  0  0   a3b 0   0   0 |
|b -ab2 -abc -abd -b3  -b2c -b2d -bc2 -bcd -bd2 0  0  a4 0  0   0   a3b 0   0 |
|  a2b  a2c  a2d  ab2  abc  abd  ac2  acd  ad2  0  0  0  a4 0   0   0   a3b 0 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|d a2bc3-a2b2d2 a2bc2-a3cd a2b3c-a4c2 a3c3-a2b2cd a2c4-a2bcd2 a2bcd-a3d2 a2b3d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|          0           0                 0 0 0 0 0 0           0 0 0 0 0 0 0 0|
|3c2+a2b2d -a2c3+a2bd2 -a2c3+ab2cd+a2bd2 0 0 0 0 0 -abc3+a2c2d 0 0 0 0 0 0 0 0|
|b3-a4c    0           ab3c+a2b2d        0 0 0 0 0 -ab3d+a3cd  0 0 0 0 0 0 0 0|
|          a2b3-a4c    -a4c              0 0 0 0 0 ab4-a3bc    0 0 0 0 0 0 0 0|
|-----------------------------------------------------------------------------|
|b4cd2 b2c4d-b3cd3 b3cd2-ab2d3 b5d2-a2b2cd2 ab2c2d2-b4d3 b2c3d2-b3d4 b2c4-abc3|
|                                                                             |
|                                                                             |
|cd -a3c2d -a2bcd2 -a2c3d -a2b2d2 -a3cd2 -a2bd3 -a2c2d2 -ab5 -a2b3c -ab4d -ab3|
|   a2cd2  0       0      a2cd2   a2d3   0      0       ab3c ab3d   0     0   |
|   a2bcd  -a2c2d  -a2cd2 a3d2    a2bd2  -a2cd2 -a2d3   a2b3 ab4    -ab3c -ab3|
|   0      a3cd    a2bcd  0       0      a3d2   a2bd2   0    0      a2b3  ab4 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|cd2 0   0   0   d3 0  0  0  |) <----- 0 : {-2, 4}                            |
|0   cd2 0   0   0  d3 0  0  |     0                                          |
|0   0   cd2 0   0  0  d3 0  |                                                |
|0   0   0   cd2 0  0  0  d3 |                                                |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|------------------------------------------------ cokernel {3} | d c b a 0 0 0|
|3} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 d c b|
|3} | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 |            {3} | 0 0 0 0 0 0 0|
|3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                               |
|                                                                             |
| 0    0    0    ad3 0   0   0   b4 0  0  0  b3c 0   0   0   b3d 0   0   0   b|
| acd2 0    0    0   ad3 0   0   0  b4 0  0  0   b3c 0   0   0   b3d 0   0   0|
| 0    acd2 0    0   0   ad3 0   0  0  b4 0  0   0   b3c 0   0   0   b3d 0   0|
| 0    0    acd2 0   0   0   ad3 0  0  0  b4 0   0   0   b3c 0   0   0   b3d 0|
|                                                                             |
|c 0   0   0   a3d 0   0   0   a2b2 0    0    0    a2bc 0    0    0    a2bd 0 |
|  a3c 0   0   0   a3d 0   0   0    a2b2 0    0    0    a2bc 0    0    0    a2|
|  0   a3c 0   0   0   a3d 0   0    0    a2b2 0    0    0    a2bc 0    0    0 |
|  0   0   a3c 0   0   0   a3d 0    0    0    a2b2 0    0    0    a2bc 0    0 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-a4cd a3c2d-a2b2d2 a2c3d-a2bd3 ab3c-a2b2d ab5-a3b2c a2b2c2-ab4d ab2c3-ab3d2 a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0 0 0 0 0 0 0 0          0           0           0                0 0 0 0 0 |
| 0 0 0 0 0 0 0 -ab2c2+b4d -a2bc2+ab3d -abc3+a2c2d -abc3+b3cd+a2c2d 0 0 0 0 0 |
| 0 0 0 0 0 0 0 b5-a2b2c   ab4-a3bc    -ab3d+a3cd  b4c+a3cd         0 0 0 0 0 |
| 0 0 0 0 0 0 0 0          0           ab4-a3bc    -a3bc            0 0 0 0 0 |
|-----------------------------------------------------------------------------|
|d b4c3-a2bc4 abc5-b3c3d bc6-b2c3d2 b2c3d-abc2d2 b4c2d-a2bc3d abc4d-b3c2d2 bc5|
|                                                                             |
|                                                                             |
|c2 -ab4c -a2b2c2 -ab3cd -ab2c3 -ab4d -a2b2cd -ab3d2 -ab2c2d -ab3c2 -a2bc3 -ab|
|   ab2c2 ab2cd   0      0      ab2cd ab2d2   0      0       abc3   abc2d  0  |
|d  a2b2c ab3c    -ab2c2 -ab2cd a2b2d ab3d    -ab2cd -ab2d2  a2bc2  ab2c2  -ab|
|   0     0       a2b2c  ab3c   0     0       a2b2d  ab3d    0      0      a2b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0    bc3 0   0   0   bc|
|    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0   bc3 0   0   0 |
|    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0   0   bc3 0   0 |
|    0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0   0   0   bc3 0 |
|                                                                             |
|   0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0    0    ab3 |
|bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0    0   |
|   a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0   |
|   0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0   |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|b2c2-a2bcd ab4c-a3bc2 a2bc3-ab3cd abc4-ab2cd2 ab2cd-a2bd2 ab4d-a3bcd a2bc2d-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0           0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a3b2 -a4c -a3bd -a3c2 -a|
|-b2c3+abc2d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a3c   a3d  0     0     a2|
|-b4d+a2bcd  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a4    a3b  -a3c  -a3d  a3|
|b5-a2b2c    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0     0    a4    a3b   0 |
|-----------------------------------------------------------------------------|
|d-b2c2d3 b2c2d2-abcd3 b4cd2-a2bc2d2 abc3d2-b3cd3 bc4d2-b2cd4 b2cd3-abd4 b4d3-|
|                                                                             |
|                                                                             |
|2c2d -abc4  -ab3cd -a2bc2d -ab2cd2 -abc3d -ab3d2 -a2bcd2 -ab2d3 -abc2d2 -ab2c|
|     0      abc2d  abcd2   0       0      abcd2  abd3    0      0       ac4  |
|c3   -abc2d a2bcd  ab2cd   -abc2d  -abcd2 a2bd2  ab2d2   -abcd2 -abd3   a2c3 |
|c2   ab2c2  0      0       a2bcd   ab2cd  0      0       a2bd2  ab2d2   0    |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | : {-3|
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 |      |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a |      |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2d 0    0    0    bcd2 0    0    0    bd3 0   0   0   c4 0  0  0  c3d 0   0  |
|   bc2d 0    0    0    bcd2 0    0    0   bd3 0   0   0  c4 0  0  0   c3d 0  |
|   0    bc2d 0    0    0    bcd2 0    0   0   bd3 0   0  0  c4 0  0   0   c3d|
|   0    0    bc2d 0    0    0    bcd2 0   0   0   bd3 0  0  0  c4 0   0   0  |
|                                                                             |
|0   0   0   ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd |
|ab3 0   0   0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    |
|0   ab3 0   0    0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    |
|0   0   ab3 0    0    0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|b3d2 abc3d-ab2d3 abc3-a2c2d ab3c2-a3c3 a2c4-ab2c2d ac5-abc2d2 abc2d-a2cd2 ab3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2b3 -a3bc -a2b2d -a2bc2 -a2b2c -a3c2 -a2bcd -a2c3 -a2b2d -a3cd -a2bd2 -a2c2d |
|bc  a2bd  0      0      a2c2   a2cd  0      0     a2cd   a2d2  0      0      |
|b   a2b2  -a2bc  -a2bd  a3c    a2bc  -a2c2  -a2cd a3d    a2bd  -a2cd  -a2d2  |
|    0     a3b    a2b2   0      0     a3c    a2bc  0      0     a3d    a2bd   |
|-----------------------------------------------------------------------------|
|a2bcd3 abc2d3-b3d4 bc3d3-b2d5 bc5-ac4d b3c4-a2c5 ac6-b2c4d c7-bc4d2 bc4d-ac3d|
|                                                                             |
|                                                                             |
|3 -a2c4 -abc3d -ac5  -ab2c2d -a2c3d -abc2d2 -ac4d  -ab2cd2 -a2c2d2 -abcd3 -ac|
|  ac3d  0      0     ac3d    ac2d2  0       0      ac2d2   acd3    0      0  |
|  abc3  -ac4   -ac3d a2c2d   abc2d  -ac3d   -ac2d2 a2cd2   abcd2   -ac2d2 -ac|
|  0     a2c3   abc3  0       0      a2c2d   abc2d  0       0       a2cd2  abc|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|, 3}                                                                         |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0   c2d2 0    0    0    cd3 0   0   0   d4 0  0  0  |, {2} | -a2b2 -a3c -a2b|
| 0   0    c2d2 0    0    0   cd3 0   0   0  d4 0  0  |  {3} | a2c   a2d  0   |
| 0   0    0    c2d2 0    0   0   cd3 0   0  0  d4 0  |  {3} | a3    a2b  -a2c|
| c3d 0    0    0    c2d2 0   0   0   cd3 0  0  0  d4 |  {3} | 0     0    a3  |
|                                                                             |
|0    0    0    abd2 0    0    0    ac3 0   0   0   ac2d 0    0    0    acd2 0|
|abcd 0    0    0    abd2 0    0    0   ac3 0   0   0    ac2d 0    0    0    a|
|0    abcd 0    0    0    abd2 0    0   0   ac3 0   0    0    ac2d 0    0    0|
|0    0    abcd 0    0    0    abd2 0   0   0   ac3 0    0    0    ac2d 0    0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|cd-a3c2d a2c3d-ab2cd2 ac4d-abcd3 abcd2-a2d3 ab3d2-a3cd2 a2c2d2-ab2d3 ac3d2-ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-ab4 -a2b2c -ab3d -ab2c2 -ab3c -a2bc2 -ab2cd -abc3 -ab3d -a2bcd -ab2d2 -abc2d|
|ab2c ab2d   0     0      abc2  abcd   0      0     abcd  abd2   0      0     |
|a2b2 ab3    -ab2c -ab2d  a2bc  ab2c   -abc2  -abcd a2bd  ab2d   -abcd  -abd2 |
|0    0      a2b2  ab3    0     0      a2bc   ab2c  0     0      a2bd   ab2d  |
|-----------------------------------------------------------------------------|
|2 b3c3d-a2c4d ac5d-b2c3d2 c6d-bc3d3 bc3d2-ac2d3 b3c2d2-a2c3d2 ac4d2-b2c2d3 c5|
|                                                                             |
|                                                                             |
|3d2 -ab2d3 -a2cd3 -abd4 -ac2d3 -b6 -ab4c -b5d -b4c2 -b5c -ab3c2 -b4cd -b3c3 -|
|    acd3   ad4    0     0      b4c b4d   0    0     b3c2 b3cd   0     0     b|
|d3  a2d3   abd3   -acd3 -ad4   ab4 b5    -b4c -b4d  ab3c b4c    -b3c2 -b3cd a|
|d2  0      0      a2d3  abd3   0   0     ab4  b5    0    0      ab3c  b4c   0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|d -a2c2 -ab3 -a2bc -ab2d -abc2 -ab2c -a2c2 -abcd -ac3 -ab2d -a2cd -abd2 -ac2d|
|  0     abc  abd   0     0     ac2   acd   0     0    acd   ad2   0     0    |
|  -a2d  a2b  ab2   -abc  -abd  a2c   abc   -ac2  -acd a2d   abd   -acd  -ad2 |
|  a2b   0    0     a2b   ab2   0     0     a2c   abc  0     0     a2d   abd  |
|                                                                             |
|    0    0    ad3 0   0   0   b4 0  0  0  b3c 0   0   0   b3d 0   0   0   b2c|
|cd2 0    0    0   ad3 0   0   0  b4 0  0  0   b3c 0   0   0   b3d 0   0   0  |
|    acd2 0    0   0   ad3 0   0  0  b4 0  0   0   b3c 0   0   0   b3d 0   0  |
|    0    acd2 0   0   0   ad3 0  0  0  b4 0   0   0   b3c 0   0   0   b3d 0  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|d4 b4c-ab3d b6-a2b3c ab3c2-b5d b3c3-b4d2 b3c2-ab2cd b5c-a2b2c2 ab2c3-b4cd b2c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| -ab2c2 -a2c3 -abc2d -ac4  -ab2cd -a2c2d -abcd2 -ac3d -ab2d2 -a2cd2 -abd3 -ac|
| ac3    ac2d  0      0     ac2d   acd2   0      0     acd2   ad3    0     0  |
| a2c2   abc2  -ac3   -ac2d a2cd   abcd   -ac2d  -acd2 a2d2   abd2   -acd2 -ad|
| 0      0     a2c2   abc2  0      0      a2cd   abcd  0      0      a2d2  abd|
|-----------------------------------------------------------------------------|
|d2-bc2d4 bc2d3-acd4 b3cd3-a2c2d3 ac3d3-b2cd4 c4d3-bcd5 bcd4-ad5 b3d4-a2cd4 ac|
|                                                                             |
|                                                                             |
|b5d -ab3cd -b4d2 -b3c2d -b4c2 -ab2c3 -b3c2d -b2c4  -b4cd -ab2c2d -b3cd2 -b2c3|
|3cd b3d2   0     0      b2c3  b2c2d  0      0      b2c2d b2cd2   0      0    |
|b3d b4d    -b3cd -b3d2  ab2c2 b3c2   -b2c3  -b2c2d ab2cd b3cd    -b2c2d -b2cd|
|    0      ab3d  b4d    0     0      ab2c2  b3c2   0     0       ab2cd  b3cd |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| -b4 -ab2c -b3d -b2c2 -b3c -abc2 -b2cd -bc3 -b3d -abcd -b2d2 -bc2d -b2c2 -ac3|
| b2c b2d   0    0     bc2  bcd   0     0    bcd  bd2   0     0     c3    c2d |
| ab2 b3    -b2c -b2d  abc  b2c   -bc2  -bcd abd  b2d   -bcd  -bd2  ac2   bc2 |
| 0   0     ab2  b3    0    0     abc   b2c  0    0     abd   b2d   0     0   |
|                                                                             |
|2 0    0    0    b2cd 0    0    0    b2d2 0    0    0    bc3 0   0   0   bc2d|
|  b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0   bc3 0   0   0   |
|  0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0   0   bc3 0   0   |
|  0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0   0   0   bc3 0   |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|4-b3cd2 b3cd-ab2d2 b5d-a2b2cd ab2c2d-b4d2 b2c3d-b3d3 b2c3-abc2d b4c2-a2bc3 ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2d2 -b5 -ab3c -b4d -b3c2 -b4c -ab2c2 -b3cd -b2c3 -b4d -ab2cd -b3d2 -b2c2d -b3|
|    b3c b3d   0    0     b2c2 b2cd   0     0     b2cd b2d2   0     0      bc3|
|3   ab3 b4    -b3c -b3d  ab2c b3c    -b2c2 -b2cd ab2d b3d    -b2cd -b2d2  abc|
|2   0   0     ab3  b4    0    0      ab2c  b3c   0    0      ab2d  b3d    0  |
|-----------------------------------------------------------------------------|
|2d4-b2d5 c3d4-bd6 0 |, | a4bc-a5d a4b3-a6c a5c2-a4b2d a4c3-a4bd2 a3b2c-a4bd a|
|                                                                             |
|                                                                             |
|d -b4d2 -ab2cd2 -b3d3  -b2c2d2 -b3c3 -abc4 -b2c3d -bc5  -b3c2d -abc3d -b2c2d2|
|  b2cd2 b2d3    0      0       bc4   bc3d  0      0     bc3d   bc2d2  0      |
|2 ab2d2 b3d2    -b2cd2 -b2d3   abc3  b2c3  -bc4   -bc3d abc2d  b2c2d  -bc3d  |
|  0     0       ab2d2  b3d2    0     0     abc3   b2c3  0      0      abc2d  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| -bc2d -c4  -b2cd -ac2d -bcd2 -c3d -b2d2 -acd2 -bd3 -c2d2 a4 0  0  0  a3b 0  |
| 0     0    c2d   cd2   0     0    cd2   d3    0    0     0  a4 0  0  0   a3b|
| -c3   -c2d acd   bcd   -c2d  -cd2 ad2   bd2   -cd2 -d3   0  0  a4 0  0   0  |
| ac2   bc2  0     0     acd   bcd  0     0     ad2  bd2   0  0  0  a4 0   0  |
|                                                                             |
| 0    0    0    bcd2 0    0    0    bd3 0   0   0   c4 0  0  0  c3d 0   0   0|
| bc2d 0    0    0    bcd2 0    0    0   bd3 0   0   0  c4 0  0  0   c3d 0   0|
| 0    bc2d 0    0    0    bcd2 0    0   0   bd3 0   0  0  c4 0  0   0   c3d 0|
| 0    0    bc2d 0    0    0    bcd2 0   0   0   bd3 0  0  0  c4 0   0   0   c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|c4-b3c2d bc5-b2c2d2 b2c2d-abcd2 b4cd-a2bc2d abc3d-b3cd2 bc4d-b2cd3 b2cd2-abd3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|c2 -abc3 -b2c2d -bc4  -b3cd -abc2d -b2cd2 -bc3d -b3d2 -abcd2 -b2d3 -bc2d2 -b2|
|   bc2d  0      0     bc2d  bcd2   0      0     bcd2  bd3    0     0      c4 |
|2  b2c2  -bc3   -bc2d abcd  b2cd   -bc2d  -bcd2 abd2  b2d2   -bcd2 -bd3   ac3|
|   0     abc2   b2c2  0     0      abcd   b2cd  0     0      abd2  b2d2   0  |
|-----------------------------------------------------------------------------|
|3b4-a5bc a4bc2-a3b3d a3bc3-a3b2d2 a3bc2-a4cd a3b3c-a5c2 a4c3-a3b2cd a3c4-a3bc|
|                                                                             |
|                                                                             |
| -bc4d  -b3cd2 -abc2d2 -b2cd3 -bc3d2 -b3d3 -abcd3 -b2d4 -bc2d3 -b2c4 -ac5 -bc|
| 0      bc2d2  bcd3    0      0      bcd3  bd4    0     0      c5    c4d  0  |
| -bc2d2 abcd2  b2cd2   -bc2d2 -bcd3  abd3  b2d3   -bcd3 -bd4   ac4   bc4  -c5|
| b2c2d  0      0       abcd2  b2cd2  0     0      abd3  b2d3   0     0    ac4|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0   0   a3c 0   0   0   a3d 0   0   0   a2b2 0    0    0    a2bc 0    0    0|
| 0   0   0   a3c 0   0   0   a3d 0   0   0    a2b2 0    0    0    a2bc 0    0|
| a3b 0   0   0   a3c 0   0   0   a3d 0   0    0    a2b2 0    0    0    a2bc 0|
| 0   a3b 0   0   0   a3c 0   0   0   a3d 0    0    0    a2b2 0    0    0    a|
|                                                                             |
|   c2d2 0    0    0    cd3 0   0   0   d4 0  0  0  |) <----- 0 : {-3, 5}     |
|   0    c2d2 0    0    0   cd3 0   0   0  d4 0  0  |     0                   |
|   0    0    c2d2 0    0   0   cd3 0   0  0  d4 0  |                         |
|3d 0    0    0    c2d2 0   0   0   cd3 0  0  0  d4 |                         |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| b4d2-a2bcd2 abc2d2-b3d3 bc3d2-b2d4 bc4-ac3d b3c3-a2c4 ac5-b2c3d c6-bc3d2 bc3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|c3 -ac4 -bc3d -c5  -b2c2d -ac3d -bc2d2 -c4d  -b2cd2 -ac2d2 -bcd3 -c3d2 -b2d3 |
|   c3d  0     0    c3d    c2d2  0      0     c2d2   cd3    0     0     cd3   |
|   bc3  -c4   -c3d ac2d   bc2d  -c3d   -c2d2 acd2   bcd2   -c2d2 -cd3  ad3   |
|   0    ac3   bc3  0      0     ac2d   bc2d  0      0      acd2  bcd2  0     |
|-----------------------------------------------------------------------------|
|d2 a3bcd-a4d2 a3b3d-a5cd a4c2d-a3b2d2 a3c3d-a3bd3 a2b3c-a3b2d a2b5-a4b2c a3b2|
|                                                                             |
|                                                                             |
|4d -c6  -b2c3d -ac4d -bc3d2 -c5d  -b2c2d2 -ac3d2 -bc2d3 -c4d2 -b2cd3 -ac2d3 -|
|   0    c4d    c3d2  0      0     c3d2    c2d3   0      0     c2d3   cd4    0|
|   -c4d ac3d   bc3d  -c4d   -c3d2 ac2d2   bc2d2  -c3d2  -c2d3 acd3   bcd3   -|
|   bc4  0      0     ac3d   bc3d  0       0      ac2d2  bc2d2 0      0      a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0  |
|    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0  |
|    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d|
|2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|d-ac2d2 b3c2d-a2c3d ac4d-b2c2d2 c5d-bc2d3 bc2d2-acd3 b3cd2-a2c2d2 ac3d2-b2cd3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-acd3 -bd4 -c2d3 0 0 0 0 |, {2} | -a3b2 -a4c -a3bd -a3c2 -a2b3 -a3bc -a2b2d -|
|d4    0    0     0 0 0 0 |  {3} | a3c   a3d  0     0     a2bc  a2bd  0      0|
|bd3   -cd3 -d4   0 0 0 0 |  {3} | a4    a3b  -a3c  -a3d  a3b   a2b2  -a2bc  -|
|0     ad3  bd3   0 0 0 0 |  {3} | 0     0    a4    a3b   0     0     a3b    a|
|-----------------------------------------------------------------------------|
|c2-a2b4d a2b2c3-a2b3d2 a2b2c2-a3bcd a2b4c-a4bc2 a3bc3-a2b3cd a2bc4-a2b2cd2 a2|
|                                                                             |
|                                                                             |
|bcd4 -c3d3 -b2d4 -acd4 -bd5 -c2d4 0 0 0 0 |) <----- 0 : {-5, 6}              |
|     0     cd4   d5    0    0     0 0 0 0 |     0                            |
|c2d3 -cd4  ad4   bd4   -cd4 -d5   0 0 0 0 |                                  |
|cd3  bcd3  0     0     ad4  bd4   0 0 0 0 |                                  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|  0    ab3 0   0   0   ab2c 0    0    0    ab2d 0    0    0    abc2 0    0   |
|  0    0   ab3 0   0   0    ab2c 0    0    0    ab2d 0    0    0    abc2 0   |
|2 0    0   0   ab3 0   0    0    ab2c 0    0    0    ab2d 0    0    0    abc2|
|  a2d2 0   0   0   ab3 0    0    0    ab2c 0    0    0    ab2d 0    0    0   |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| c4d2-bcd4 bcd3-ad4 b3d3-a2cd3 ac2d3-b2d4 c3d3-bd5 0 |) <--------------------|
|                                                           {4} | 1 0 0 0 0 0 |
|                                                           {4} | 0 1 0 0 0 0 |
|                                                           {4} | 0 0 1 0 0 0 |
|                                                           {4} | 0 0 0 1 0 0 |
|                                                           {4} | 0 0 0 0 1 0 |
|                                                           {4} | 0 0 0 0 0 1 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {4} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {5} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {6} | 0 0 0 0 0 0 |
|                                                           {0} | 0 0 0 0 0 0 |
|                                                                             |
|a2bc2 -a2b2c -a3c2 -a2bcd -a2c3 -a2b2d -a3cd -a2bd2 -a2c2d -ab4 -a2b2c -ab3d |
|      a2c2   a2cd  0      0     a2cd   a2d2  0      0      ab2c ab2d   0     |
|a2bd  a3c    a2bc  -a2c2  -a2cd a3d    a2bd  -a2cd  -a2d2  a2b2 ab3    -ab2c |
|2b2   0      0     a3c    a2bc  0      0     a3d    a2bd   0    0      a2b2  |
|-----------------------------------------------------------------------------|
|b2cd-a3bd2 a2b4d-a4bcd a3bc2d-a2b3d2 a2bc3d-a2b2d3 a2bc3-a3c2d a2b3c2-a4c3 a3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0    abcd 0    0    0    abd2 0    0    0    ac3 0   0   0   ac2d 0    0    |
| 0    0    abcd 0    0    0    abd2 0    0    0   ac3 0   0   0    ac2d 0    |
| 0    0    0    abcd 0    0    0    abd2 0    0   0   ac3 0   0    0    ac2d |
| abc2 0    0    0    abcd 0    0    0    abd2 0   0   0   ac3 0    0    0    |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|------------------------------------------------------------- cokernel {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 |            {4} | |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  |
|                                                                             |
|-ab2c2 -ab3c -a2bc2 -ab2cd -abc3 -ab3d -a2bcd -ab2d2 -abc2d -ab2c2 -a2c3 -abc|
|0      abc2  abcd   0      0     abcd  abd2   0      0      ac3    ac2d  0   |
|-ab2d  a2bc  ab2c   -abc2  -abcd a2bd  ab2d   -abcd  -abd2  a2c2   abc2  -ac3|
|ab3    0     0      a2bc   ab2c  0     0      a2bd   ab2d   0      0     a2c2|
|-----------------------------------------------------------------------------|
|c4-a2b2c2d a2c5-a2bc2d2 a2bc2d-a3cd2 a2b3cd-a4c2d a3c3d-a2b2cd2 a2c4d-a2bcd3 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0    acd2 0    0    0    ad3 0   0   0   b4 0  0  0  b3c 0   0   0   b3d 0   |
|0    0    acd2 0    0    0   ad3 0   0   0  b4 0  0  0   b3c 0   0   0   b3d |
|0    0    0    acd2 0    0   0   ad3 0   0  0  b4 0  0   0   b3c 0   0   0   |
|ac2d 0    0    0    acd2 0   0   0   ad3 0  0  0  b4 0   0   0   b3c 0   0   |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-d -b -d -c 0  0  -d 0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0 |
|c  a  0  0  0  -d 0  -d -b 0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0 |
|0  0  b  a  -d 0  0  0  0  0  -d 0  0  0  0  0  -d -c 0  0  -d 0  0  0  0  0 |
|0  0  0  0  c  b  a  0  0  -d 0  0  0  -d 0  0  0  0  0  -d 0  0  0  -d 0  0 |
|0  0  0  0  0  0  0  c  a  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  -d -b|
|0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  0  0  0  0  0  0  -d 0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  b  a  -d 0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  -d 0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  a |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|2d -ac4  -ab2cd -a2c2d -abcd2 -ac3d -ab2d2 -a2cd2 -abd3 -ac2d2 -b5 -ab3c -b4d|
|   0     ac2d   acd2   0      0     acd2   ad3    0     0      b3c b3d   0   |
|   -ac2d a2cd   abcd   -ac2d  -acd2 a2d2   abd2   -acd2 -ad3   ab3 b4    -b3c|
|   abc2  0      0      a2cd   abcd  0      0      a2d2  abd2   0   0     ab3 |
|-----------------------------------------------------------------------------|
|a2bcd2-a3d3 a2b3d2-a4cd2 a3c2d2-a2b2d3 a2c3d2-a2bd4 ab4c-a2b3d ab6-          |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0   0   b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0             |
|0   0   0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0             |
|b3d 0   0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0             |
|0   b3d 0    0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2          |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0            |
| 0  -d 0  0  0  0  0  0  0  -d 0  0  0  0  -d 0  0  0  0  0  0  0            |
| 0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| -d 0  0  0  -d 0  0  0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0            |
| 0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  -d -c 0  0            |
| 0  0  0  0  0  0  0  -d 0  0  0  0  -d 0  0  0  0  0  0  0  0  -d           |
| 0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0  0  0            |
| 0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| d  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  c  b  a  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0            |
| 0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  b  a  -d 0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0            |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| -b3c2 -b4c -ab2c2 -b3cd -b2c3 -b4d -ab2cd -b3d2 -b2c2d -b3c2 -abc3          |
| 0     b2c2 b2cd   0     0     b2cd b2d2   0     0      bc3   bc2d           |
| -b3d  ab2c b3c    -b2c2 -b2cd ab2d b3d    -b2cd -b2d2  abc2  b2c2           |
| b4    0    0      ab2c  b3c   0    0      ab2d  b3d    0     0              |
|-----------------------------------------------------------------------------|
|a3b3c a2b3c2-ab5d ab3c3-ab4d2 ab3c2-a2b2cd ab5c-a3b2c2 a2b2c3-ab4cd ab2c4-ab3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| bc3 0   0   0   bc2d 0    0    0    bcd2 0    0    0    bd3 0   0   0   c4 0|
| 0   bc3 0   0   0    bc2d 0    0    0    bcd2 0    0    0   bd3 0   0   0  c|
| 0   0   bc3 0   0    0    bc2d 0    0    0    bcd2 0    0   0   bd3 0   0  0|
| 0   0   0   bc3 0    0    0    bc2d 0    0    0    bcd2 0   0   0   bd3 0  0|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  -d 0  0  0  0  -d 0  0 |
|-d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  0 |
|0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  -d 0  0  0  0  -d 0  0  0  0 |
|0  0  0  0  0  0  0  -d -b 0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  -d 0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  -d 0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|a  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  c  b  a  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  c  a  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  0  0  0  0  0  0  0  0  0  -d|
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  d  c  b  a  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| -b2c2d -bc4  -b3cd -abc2d -b2cd2 -bc3d -b3d2 -abcd2 -b2d3 -bc2d2 -b2c3 -ac4 |
| 0      0     bc2d  bcd2   0      0     bcd2  bd3    0     0      c4    c3d  |
| -bc3   -bc2d abcd  b2cd   -bc2d  -bcd2 abd2  b2d2   -bcd2 -bd3   ac3   bc3  |
| abc2   b2c2  0     0      abcd   b2cd  0     0      abd2  b2d2   0     0    |
|-----------------------------------------------------------------------------|
|cd2 ab3cd-a2b2d2 ab5d-a3b2cd a2b2c2d-ab4d2 ab2c3d-ab3d3 ab2c3-a2bc2d ab4c2-  |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|  0  0  c3d 0   0   0   c2d2 0    0    0    cd3 0   0   0   d4 0  0  0  |)   |
|4 0  0  0   c3d 0   0   0    c2d2 0    0    0   cd3 0   0   0  d4 0  0  |    |
|  c4 0  0   0   c3d 0   0    0    c2d2 0    0   0   cd3 0   0  0  d4 0  |    |
|  0  c4 0   0   0   c3d 0    0    0    c2d2 0   0   0   cd3 0  0  0  d4 |    |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  -d 0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  -d 0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0   |
| 0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  -d -c 0  0  -d 0  0  0  0   |
| 0  -d 0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  -d 0   |
| 0  0  0  0  0  -d 0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  -d 0  0   |
| 0  0  0  0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| a  0  0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0   |
| 0  d  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  0  0  0  0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  b  a  -d 0  0  0  0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  -d 0  0  0   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  -d  |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c   |
| 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-bc3d -c5  -b2c2d -ac3d -bc2d2 -c4d  -b2cd2 -ac2d2 -bcd3 -c3d2 -b2d3 -acd3   |
|0     0    c3d    c2d2  0      0     c2d2   cd3    0     0     cd3   d4      |
|-c4   -c3d ac2d   bc2d  -c3d   -c2d2 acd2   bcd2   -c2d2 -cd3  ad3   bd3     |
|ac3   bc3  0      0     ac2d   bc2d  0      0      acd2  bcd2  0     0       |
|-----------------------------------------------------------------------------|
|a3bc3 a2bc4-ab3c2d abc5-ab2c2d2 ab2c2d-a2bcd2 ab4cd-a3bc2d a2bc3d-ab3cd2     |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|<----- 0 : {-3, 4}                                                           |
|   0                                                                         |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
| 0  0  0  0  0  c2  -ac 0   0   -cd -ad 0   0   0   -d2 -bd 0   0   0        |
| 0  0  0  0  0  -bd b2  -d2 0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   c2  cd  0   0   0   0   -d2 0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   -d2 0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   -d2 bd  b2  0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   -d2 0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   cd  c2  0   0   0   -d2 0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   -d2      |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   d2  bd  b2  0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   d2  0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   -d2 0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   d2  cd       |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  -d 0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| -d 0  0  0  -d 0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  -d 0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| b  a  -d 0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
| 0  0  c  b  a  0   0   0   0   0   0   0   0   0   0   0   0   0   0        |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-bd4 -c2d3 0 0 0 0 |) <----- 0 : {-4, 5}                                     |
|0    0     0 0 0 0 |     0                                                   |
|-cd3 -d4   0 0 0 0 |                                                         |
|ad3  bd3   0 0 0 0 |                                                         |
|-----------------------------------------------------------------------------|
| abc4d-ab2cd3 ab2cd2-a2bd3 ab4d2-a3bcd2 a2bc2d2-ab3d3 abc3d2-ab2d4 abc4-a2c3d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|0   0   0   0   0   0   0   0   0   0   | : {-4, 4}                          |
|0   0   -d2 -bd 0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   -d2 0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|-d2 0   0   0   -d2 0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|c2  0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   -d2 0   0   -d2 0   |                                    |
|0   0   0   0   0   0   0   -d2 0   0   |                                    |
|0   0   0   0   0   0   -d2 0   0   0   |                                    |
|0   d2  bd  b2  0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   d2  0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   d2  0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   -d2 |                                    |
|0   0   0   0   0   0   d2  cd  c2  0   |                                    |
|0   0   0   0   0   0   0   0   0   d2  |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|0   0   0   0   0   0   0   0   0   0   |                                    |
|-----------------------------------------------------------------------------|
|ab3c3-a3c4 a2c5-ab2c3d ac6-abc3d2 abc3d-a2c2d2 ab3c2d-a3c3d a2c4d-ab2c2d2    |
|                                                                             |
|-----------------------------------------------------------------------------|
|ac5d-abc2d3 abc2d2-a2cd3 ab3cd2-a3c2d2 a2c3d2-ab2cd3 ac4d2-abcd4 abcd3-a2d4  |
|                                                                             |
|-----------------------------------------------------------------------------|
|ab3d3-a3cd3 a2c2d3-ab2d4 ac3d3-abd5 b5c-ab4d b7-a2b4c ab4c2-b6d b4c3-b5d2    |
|                                                                             |
|-----------------------------------------------------------------------------|
|b4c2-ab3cd b6c-a2b3c2 ab3c3-b5cd b3c4-b4cd2 b4cd-ab3d2 b6d-a2b3cd ab3c2d-b5d2|
|                                                                             |
|-----------------------------------------------------------------------------|
|b3c3d-b4d3 b3c3-ab2c2d b5c2-a2b2c3 ab2c4-b4c2d b2c5-b3c2d2 b3c2d-ab2cd2      |
|                                                                             |
|-----------------------------------------------------------------------------|
|b5cd-a2b2c2d ab2c3d-b4cd2 b2c4d-b3cd3 b3cd2-ab2d3 b5d2-a2b2cd2 ab2c2d2-b4d3  |
|                                                                             |
|-----------------------------------------------------------------------------|
|b2c3d2-b3d4 b2c4-abc3d b4c3-a2bc4 abc5-b3c3d bc6-b2c3d2 b2c3d-abc2d2         |
|                                                                             |
|-----------------------------------------------------------------------------|
|b4c2d-a2bc3d abc4d-b3c2d2 bc5d-b2c2d3 b2c2d2-abcd3 b4cd2-a2bc2d2 abc3d2-b3cd3|
|                                                                             |
|-----------------------------------------------------------------------------|
|bc4d2-b2cd4 b2cd3-abd4 b4d3-a2bcd3 abc2d3-b3d4 bc3d3-b2d5 bc5-ac4d b3c4-a2c5 |
|                                                                             |
|-----------------------------------------------------------------------------|
|ac6-b2c4d c7-bc4d2 bc4d-ac3d2 b3c3d-a2c4d ac5d-b2c3d2 c6d-bc3d3 bc3d2-ac2d3  |
|                                                                             |
|-----------------------------------------------------------------------------|
|b3c2d2-a2c3d2 ac4d2-b2c2d3 c5d2-bc2d4 bc2d3-acd4 b3cd3-a2c2d3 ac3d3-b2cd4    |
|                                                                             |
|-----------------------------------------------------------------------------|
|c4d3-bcd5 bcd4-ad5 b3d4-a2cd4 ac2d4-b2d5 c3d4-bd6 0 |) <----- 0 : {-5, 5}    |
|                                                          0                  |
+-----------------------------------------------------------------------------+

See also
========

  * prune(SpectralSequence),
    -- a minimal presentation of a spectral sequence
  * SpectralSequencePage -- the type of all
    spectral sequence pages
  * PageMap -- the type of all page maps

Ways to use this method:
========================

  * pruningMaps(SpectralSequencePage)
    -- compute the pruning maps on a
    spectral sequence page
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2850:0.

ReducedHomology -- name for an optional argument
************************************************

Functions with optional argument named ReducedHomology:
=======================================================

  * filteredComplex(...,ReducedHomology=>...)

For the programmer
==================

The object ReducedHomology, is a symbol (Macaulay2Doc).

-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:1055:0.

ring(Page)
**********

  * Function: ring (Macaulay2Doc),

Ways to use this method:
========================

  * ring(Page)
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2294:0.

Seeing Cancellations
********************

Here we give an example of a spectral sequence that takes n+2 steps to
degenerate, where n is the embedding dimension of the ring.  We present this
when n = 2 but the user with computational power can easily do a bigger case.

+------------------------------------------------------------+
|i1 : S = ZZ/101[x,y];                                       |
+------------------------------------------------------------+
|i2 : I = ideal(x^2,x*y,y^2);                                |
|                                                            |
|o2 : Ideal of S                                             |
+------------------------------------------------------------+
|i3 : R = S/I;                                               |
+------------------------------------------------------------+
|i4 : kR = coker vars R;                                     |
+------------------------------------------------------------+
|i5 : kS = coker vars S;                                     |
+------------------------------------------------------------+
|i6 : CS = res kS;                                           |
+------------------------------------------------------------+
|i7 : CR = res(kR,LengthLimit=>6);                           |
+------------------------------------------------------------+
|i8 : CS' = CS**R;                                           |
+------------------------------------------------------------+
|i9 : E = prune spectralSequence (CS' ** filteredComplex CR);|
+------------------------------------------------------------+

Since this spectral sequence only consists of $k$ vector spaces, and all are
generated in a single degree, for ease of presentation we may as well just look
at the rank and degree which we can easily encode in a matrix with $rt^d$
encoding the rank $r$ and degree $d$ of each vector space $E_{i,j}$.

+-----------------------------------------------------------------------------+
|i10 : use ZZ[t]                                                              |
|                                                                             |
|o10 = ZZ[t]                                                                  |
|                                                                             |
|o10 : PolynomialRing                                                         |
+-----------------------------------------------------------------------------+
|i11 : easyPresentation = (P,n,m) -> (                                        |
|         transpose matrix apply(n,                                           |
|             i-> apply(m,                                                    |
|                 j-> (length (P_{i,j}))*t^(                                  |
|                     if (L = unique flatten degrees P_{i,j})!= {} then first |
|                 )                                                           |
|             ));                                                             |
|-----------------------------------------------------------------------------|
|L else 0)                                                                    |
+-----------------------------------------------------------------------------+

To see what we're going for, we compute the E_{infinity} page and also some
earlier pages. Notice that it's clear that all terms except those in the top
row of the matrix must eventually disappear, but for this to happen, there must
a map of the right degree mapping to them.

+------------------------------------------+
|i12 : easyPresentation(E_infinity,6,3)    |
|                                          |
|o12 = {-2} | 1 2t t2 0 0    0    |        |
|      {-7} | 0 0  0  0 0    96t7 |        |
|      {-8} | 0 0  0  0 32t7 64t8 |        |
|                                          |
|                    3            6        |
|o12 : Matrix (ZZ[t])  <-- (ZZ[t])         |
+------------------------------------------+
|i13 : easyPresentation(E_1,6,3)           |
|                                          |
|o13 = {-5} | 1   2t  4t2  8t3  16t4 32t5 ||
|      {-7} | 3t2 6t3 12t4 24t5 48t6 96t7 ||
|      {-8} | 2t3 4t4 8t5  16t6 32t7 64t8 ||
|                                          |
|                    3            6        |
|o13 : Matrix (ZZ[t])  <-- (ZZ[t])         |
+------------------------------------------+
|i14 : easyPresentation(E_2,6,3)           |
|                                          |
|o14 = {-5} | 1   2t  4t2  8t3  16t4 32t5 ||
|      {-7} | 3t2 6t3 12t4 24t5 48t6 96t7 ||
|      {-8} | 2t3 4t4 8t5  16t6 32t7 64t8 ||
|                                          |
|                    3            6        |
|o14 : Matrix (ZZ[t])  <-- (ZZ[t])         |
+------------------------------------------+
|i15 : easyPresentation(E_3,6,3)           |
|                                          |
|o15 = {-5} | 1   2t  t2  2t3  4t4  8t5  | |
|      {-7} | 0   0   0   0    0    96t7 | |
|      {-8} | 2t3 4t4 8t5 16t6 32t7 64t8 | |
|                                          |
|                    3            6        |
|o15 : Matrix (ZZ[t])  <-- (ZZ[t])         |
+------------------------------------------+
|i16 : length image ((E_2).dd_{3,0})       |
|                                          |
|o16 = 6                                   |
+------------------------------------------+
|i17 : length image (E_3).dd_{3,0}         |
|                                          |
|o17 = 2                                   |
+------------------------------------------+

The final two computations are meant to explain that the copy of $k^8$ in
degree 3 that appears on the $E_1$ cancels in two steps via an $E_2$ map with
$k^6$ and via an $E_3$ map with a $k^2$.

-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:1546:0.

Shift -- name for an optional argument
**************************************

Functions with optional argument named Shift:
=============================================

  * filteredComplex(...,Shift=>...)

For the programmer
==================

The object Shift, is a symbol (Macaulay2Doc).

-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:1048:0.

sourcePruningMap
****************

For the programmer
==================

The object sourcePruningMap, is a symbol (Macaulay2Doc).

-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:1067:0.

Spectral sequences and connecting morphisms
*******************************************

If $0 \rightarrow A \rightarrow B \rightarrow C \rightarrow 0$ is a short exact
sequence of chain complexes then the connecting morphism $H_i(C) \rightarrow
H_{i - 1}(A)$ can realized as a suitable map on the $E^1$ of a spectral
sequence determined by a suitably defined two step filtration of $B$.

Here we illustrate this realization in a concrete situation:  we compute the
connecting morphism $H^i(X, F) \rightarrow H^{i + 1}(X, G)$ arising from a
short exact sequence $0 \rightarrow G \rightarrow H \rightarrow F \rightarrow
0$ of sheaves on a smooth toric variety $X$.

More specifically we let $X = \mathbb{P}^1 \times \mathbb{P}^1$ and use
multigraded commutative algebra together with spectral sequences to compute the
connecting morphism $H^1(C, OO_C(1,0)) \rightarrow H^2(X, OO_X(-2,-3))$ where
$C$ is a general divisor of type $(3,3)$ on $X$.  This connecting morphism is
an isomorphism.

+-----------------------------------------------------------------------------+
|i1 : R = ZZ/101[a_0..b_1, Degrees=>{2:{1,0},2:{0,1}}]; -- PP^1 x PP^1        |
+-----------------------------------------------------------------------------+
|i2 : M = intersect(ideal(a_0,a_1),ideal(b_0,b_1)) ; -- irrelevant ideal      |
|                                                                             |
|o2 : Ideal of R                                                              |
+-----------------------------------------------------------------------------+
|i3 : M = M_*/(x -> x^5)//ideal ; -- Suitably high Frobenius power of M       |
|                                                                             |
|o3 : Ideal of R                                                              |
+-----------------------------------------------------------------------------+
|i4 : G = res image gens M ;                                                  |
+-----------------------------------------------------------------------------+
|i5 : I = ideal random(R^1, R^{{-3,-3}}) -- ideal of C                        |
|                                                                             |
|              3 3      2   3       2 3      3 3      3 2        2   2        |
|o5 = ideal(24a b  + 19a a b  - 8a a b  - 38a b  - 36a b b  + 19a a b b  -    |
|              0 0      0 1 0     0 1 0      1 0      0 0 1      0 1 0 1      |
|     ------------------------------------------------------------------------|
|          2 2        3 2        3   2      2     2        2   2      3   2   |
|     22a a b b  - 16a b b  - 30a b b  - 10a a b b  - 29a a b b  + 39a b b  - |
|        0 1 0 1      1 0 1      0 0 1      0 1 0 1      0 1 0 1      1 0 1   |
|     ------------------------------------------------------------------------|
|        3 3      2   3        2 3      3 3                                   |
|     29a b  - 29a a b  - 24a a b  + 21a b )                                  |
|        0 1      0 1 1      0 1 1      1 1                                   |
|                                                                             |
|o5 : Ideal of R                                                              |
+-----------------------------------------------------------------------------+
|i6 : b = chainComplex gradedModule R^{{1,0}} -- make line bundle a chain     |
|                                                                             |
|      1                                                                      |
|o6 = R                                                                       |
|                                                                             |
|     0                                                                       |
|                                                                             |
|o6 : ChainComplex                                                            |
|-----------------------------------------------------------------------------|
|complex                                                                      |
+-----------------------------------------------------------------------------+
|i7 : a = chainComplex gradedModule R^{{-2,-3}}                               |
|                                                                             |
|      1                                                                      |
|o7 = R                                                                       |
|                                                                             |
|     0                                                                       |
|                                                                             |
|o7 : ChainComplex                                                            |
+-----------------------------------------------------------------------------+
|i8 : f = chainComplexMap(b, a,{random(R^1, R^{{-3,-3}})}) ;                  |
+-----------------------------------------------------------------------------+
|i9 : K = filteredComplex ({Hom(G,f)}) ; -- the two step filtered complex we  |
|-----------------------------------------------------------------------------|
|want                                                                         |
+-----------------------------------------------------------------------------+
|i10 : E = prune spectralSequence K ;                                         |
+-----------------------------------------------------------------------------+

The degree zero piece of the map $E^1 .dd_{1, -2}$ below is the desired
connecting morphism $H^1(C, OO_C(1,0)) \rightarrow H^2(X, OO_X(-2,-3))$.

+-----------------------------------------------------------------------------+
|i11 : E^1 .dd_{1,-2} -- the connecting map HH^1(C, OO_C(1,0)) --> HH^2(X, OO_|
|                                                                             |
|o11 = {-8, -7} | 0 0 -31b_0^4b_1^2-29b_0^3b_1^3+31b_0^2b_1^4                 |
|      -----------------------------------------------------------------------|
|      -22b_0^4b_1^2-9b_0^3b_1^3+34b_0^2b_1^4                                 |
|      -----------------------------------------------------------------------|
|      8b_0^4b_1^2+50b_0^3b_1^3-9b_0^2b_1^4                                   |
|      -----------------------------------------------------------------------|
|      27a_0b_0^4b_1+23a_1b_0^4b_1-35a_0b_0^3b_1^2-19a_1b_0^3b_1^2+42a_0b_0^2b|
|      -----------------------------------------------------------------------|
|      _1^3-23a_1b_0^2b_1^3-29a_0b_0b_1^4+14a_1b_0b_1^4                       |
|      -----------------------------------------------------------------------|
|      -27a_0b_0^4b_1+12a_1b_0^4b_1+23a_0b_0^3b_1^2-28a_1b_0^3b_1^2+34a_0b_0^ |
|      -----------------------------------------------------------------------|
|      2b_1^3+10a_1b_0^2b_1^3-36a_0b_0b_1^4+40a_1b_0b_1^4                     |
|      -----------------------------------------------------------------------|
|      -20a_0b_0^4b_1-2a_1b_0^4b_1+41a_0b_0^3b_1^2-46a_1b_0^3b_1^2-8a_0b_0^2b_|
|      -----------------------------------------------------------------------|
|      1^3-17a_1b_0^2b_1^3-42a_0b_0b_1^4-3a_1b_0b_1^4                         |
|      -----------------------------------------------------------------------|
|      -34a_0^2b_0^3b_1+25a_0a_1b_0^3b_1+26a_1^2b_0^3b_1-33a_0^2b_0^2b_1^2-29a|
|      -----------------------------------------------------------------------|
|      _0a_1b_0^2b_1^2+4a_1^2b_0^2b_1^2+42a_0^2b_0b_1^3-45a_0a_1b_0b_1^3-5a_1^|
|      -----------------------------------------------------------------------|
|      2b_0b_1^3-7a_0^2b_1^4+5a_0a_1b_1^4                                     |
|      -----------------------------------------------------------------------|
|      30a_0^2b_0^3b_1+22a_0a_1b_0^3b_1-28a_1^2b_0^3b_1-28a_0^2b_0^2b_1^2+32a_|
|      -----------------------------------------------------------------------|
|      0a_1b_0^2b_1^2-29a_1^2b_0^2b_1^2-9a_0^2b_0b_1^3+35a_0a_1b_0b_1^3+a_1^2b|
|      -----------------------------------------------------------------------|
|      _0b_1^3-17a_0^2b_1^4+45a_0a_1b_1^4-12a_1^2b_1^4                        |
|      -----------------------------------------------------------------------|
|      -50a_0^2b_0^3b_1-12a_0a_1b_0^3b_1-39a_1^2b_0^3b_1+35a_0^2b_0^2b_1^2+27a|
|      -----------------------------------------------------------------------|
|      _0a_1b_0^2b_1^2-2a_1^2b_0^2b_1^2+48a_0^2b_0b_1^3+33a_0a_1b_0b_1^3-36a_1|
|      -----------------------------------------------------------------------|
|      ^2b_0b_1^3+33a_0^2b_1^4-23a_0a_1b_1^4-15a_1^2b_1^4                     |
|      -----------------------------------------------------------------------|
|      -17a_0^2b_0^3b_1-5a_0a_1b_0^3b_1-13a_1^2b_0^3b_1-34a_0^2b_0^2b_1^2+26a_|
|      -----------------------------------------------------------------------|
|      0a_1b_0^2b_1^2+39a_1^2b_0^2b_1^2+38a_0^2b_0b_1^3-18a_0a_1b_0b_1^3+20a_1|
|      -----------------------------------------------------------------------|
|      ^2b_0b_1^3+47a_0^2b_1^4+47a_0a_1b_1^4-22a_1^2b_1^4                     |
|      -----------------------------------------------------------------------|
|      22a_0^3b_0^2b_1-5a_0^2a_1b_0^2b_1+25a_0a_1^2b_0^2b_1-12a_1^3b_0^2b_1+  |
|      -----------------------------------------------------------------------|
|      32a_0^3b_0b_1^2+9a_0^2a_1b_0b_1^2+10a_0a_1^2b_0b_1^2-31a_1^3b_0b_1^2-  |
|      -----------------------------------------------------------------------|
|      37a_0^3b_1^3+27a_0^2a_1b_1^3-15a_0a_1^2b_1^3+45a_1^3b_1^3              |
|      -----------------------------------------------------------------------|
|      30a_0^3b_0^2b_1-17a_0^2a_1b_0^2b_1-34a_0a_1^2b_0^2b_1-50a_1^3b_0^2b_1- |
|      -----------------------------------------------------------------------|
|      10a_0^3b_0b_1^2-10a_0^2a_1b_0b_1^2-16a_0a_1^2b_0b_1^2-37a_1^3b_0b_1^2+a|
|      -----------------------------------------------------------------------|
|      _0^3b_1^3+43a_0^2a_1b_1^3-a_0a_1^2b_1^3-11a_1^3b_1^3                   |
|      -----------------------------------------------------------------------|
|      -28a_0^3b_0^2b_1-13a_0^2a_1b_0^2b_1+26a_0a_1^2b_0^2b_1-39a_1^3b_0^2b_1+|
|      -----------------------------------------------------------------------|
|      15a_0^3b_0b_1^2+21a_0^2a_1b_0b_1^2-8a_0a_1^2b_0b_1^2+26a_1^3b_0b_1^2-  |
|      -----------------------------------------------------------------------|
|      33a_0^3b_1^3+33a_0^2a_1b_1^3+6a_0a_1^2b_1^3-5a_1^3b_1^3                |
|      -----------------------------------------------------------------------|
|      23a_0^4b_0b_1+12a_0^3a_1b_0b_1-2a_0^2a_1^2b_0b_1-2a_0a_1^3b_0b_1-44a_1^|
|      -----------------------------------------------------------------------|
|      4b_0b_1-20a_0^4b_1^2-29a_0^3a_1b_1^2+16a_0^2a_1^2b_1^2+2a_0a_1^3b_1^2- |
|      -----------------------------------------------------------------------|
|      42a_1^4b_1^2 27a_0^4b_0b_1-27a_0^3a_1b_0b_1-20a_0^2a_1^2b_0b_1+2a_0a_1^|
|      -----------------------------------------------------------------------|
|      3b_0b_1+27a_1^4b_0b_1+18a_0^4b_1^2+19a_0^3a_1b_1^2+45a_0^2a_1^2b_1^2+  |
|      -----------------------------------------------------------------------|
|      12a_0a_1^3b_1^2+7a_1^4b_1^2                                            |
|      -----------------------------------------------------------------------|
|      23a_0^2b_0^4+27a_0a_1b_0^4-44a_1^2b_0^4+9a_0^2b_0^3b_1+5a_0a_1b_0^3b_1-|
|      -----------------------------------------------------------------------|
|      30a_1^2b_0^3b_1+8a_0^2b_0^2b_1^2-21a_0a_1b_0^2b_1^2+32a_1^2b_0^2b_1^2+ |
|      -----------------------------------------------------------------------|
|      41a_0^2b_0b_1^3-14a_0a_1b_0b_1^3-35a_1^2b_0b_1^3+25a_0^2b_1^4-20a_0a_1b|
|      -----------------------------------------------------------------------|
|      _1^4+45a_1^2b_1^4 -a_0^2b_0^4+47a_0a_1b_0^4+27a_1^2b_0^4-21a_0^2b_0^3b_|
|      -----------------------------------------------------------------------|
|      1+4a_0a_1b_0^3b_1-42a_1^2b_0^3b_1-42a_0^2b_0^2b_1^2+31a_0a_1b_0^2b_1^2+|
|      -----------------------------------------------------------------------|
|      22a_1^2b_0^2b_1^2-3a_0^2b_0b_1^3+45a_0a_1b_0b_1^3-6a_1^2b_0b_1^3+21a_0^|
|      -----------------------------------------------------------------------|
|      2b_1^4-42a_0a_1b_1^4-33a_1^2b_1^4                                      |
|      -----------------------------------------------------------------------|
|      43a_0^2b_0^4-a_0a_1b_0^4+23a_1^2b_0^4+50a_0^2b_0^3b_1-32a_0a_1b_0^3b_1+|
|      -----------------------------------------------------------------------|
|      49a_1^2b_0^3b_1+35a_0^2b_0^2b_1^2+50a_0a_1b_0^2b_1^2+6a_1^2b_0^2b_1^2- |
|      -----------------------------------------------------------------------|
|      42a_0^2b_0b_1^3+3a_0a_1b_0b_1^3+20a_1^2b_0b_1^3-41a_0^2b_1^4-12a_0a_1b_|
|      -----------------------------------------------------------------------|
|      1^4-a_1^2b_1^4 9a_0^3b_0^3-39a_0^2a_1b_0^3-37a_0a_1^2b_0^3-50a_1^3b_0^3|
|      -----------------------------------------------------------------------|
|      +43a_0^3b_0^2b_1-9a_0^2a_1b_0^2b_1-8a_0a_1^2b_0^2b_1+47a_1^3b_0^2b_1+  |
|      -----------------------------------------------------------------------|
|      43a_0^3b_0b_1^2+4a_0^2a_1b_0b_1^2+35a_0a_1^2b_0b_1^2+26a_1^3b_0b_1^2+  |
|      -----------------------------------------------------------------------|
|      46a_0^3b_1^3-38a_0^2a_1b_1^3-21a_0a_1^2b_1^3-29a_1^3b_1^3              |
|      -----------------------------------------------------------------------|
|      -8a_0^3b_0^3-50a_0^2a_1b_0^3-42a_0a_1^2b_0^3-24a_1^3b_0^3+24a_0^3b_0^2b|
|      -----------------------------------------------------------------------|
|      _1-49a_0^2a_1b_0^2b_1-32a_0a_1^2b_0^2b_1-25a_1^3b_0^2b_1-4a_0^3b_0b_1^2|
|      -----------------------------------------------------------------------|
|      +35a_0^2a_1b_0b_1^2-44a_0a_1^2b_0b_1^2+13a_1^3b_0b_1^2-5a_0^3b_1^3-25a_|
|      -----------------------------------------------------------------------|
|      0^2a_1b_1^3+44a_0a_1^2b_1^3+9a_1^3b_1^3                                |
|      -----------------------------------------------------------------------|
|      -33a_0^3b_0^3-37a_0^2a_1b_0^3-23a_0a_1^2b_0^3-42a_1^3b_0^3+9a_0^3b_0^2b|
|      -----------------------------------------------------------------------|
|      _1+16a_0^2a_1b_0^2b_1-29a_0a_1^2b_0^2b_1-23a_1^3b_0^2b_1+30a_0^3b_0b_1^|
|      -----------------------------------------------------------------------|
|      2+45a_0^2a_1b_0b_1^2+27a_1^3b_0b_1^2-6a_0^3b_1^3+5a_0^2a_1b_1^3-44a_0a_|
|      -----------------------------------------------------------------------|
|      1^2b_1^3+20a_1^3b_1^3 -17a_0^3b_0^3+9a_0^2a_1b_0^3-33a_0a_1^2b_0^3-8a_1|
|      -----------------------------------------------------------------------|
|      ^3b_0^3-46a_0^3b_0^2b_1-16a_0^2a_1b_0^2b_1+32a_0a_1^2b_0^2b_1+22a_1^3b_|
|      -----------------------------------------------------------------------|
|      0^2b_1+38a_0^3b_0b_1^2-17a_0^2a_1b_0b_1^2-33a_0a_1^2b_0b_1^2+7a_1^3b_0b|
|      -----------------------------------------------------------------------|
|      _1^2+24a_0^3b_1^3-7a_0^2a_1b_1^3+28a_0a_1^2b_1^3-6a_1^3b_1^3           |
|      -----------------------------------------------------------------------|
|      -8a_0^3a_1b_0^2-50a_0^2a_1^2b_0^2-42a_0a_1^3b_0^2-24a_1^4b_0^2+25a_0^4b|
|      -----------------------------------------------------------------------|
|      _0b_1+3a_0^3a_1b_0b_1-43a_0^2a_1^2b_0b_1-15a_0a_1^3b_0b_1-46a_1^4b_0b_1|
|      -----------------------------------------------------------------------|
|      +18a_0^4b_1^2+7a_0^3a_1b_1^2-50a_0^2a_1^2b_1^2-22a_0a_1^3b_1^2+49a_1^4b|
|      -----------------------------------------------------------------------|
|      _1^2 -33a_0^3a_1b_0^2-37a_0^2a_1^2b_0^2-23a_0a_1^3b_0^2-42a_1^4b_0^2+  |
|      -----------------------------------------------------------------------|
|      17a_0^4b_0b_1-35a_0^3a_1b_0b_1+45a_0^2a_1^2b_0b_1+50a_0a_1^3b_0b_1-48a_|
|      -----------------------------------------------------------------------|
|      1^4b_0b_1+36a_0^4b_1^2-11a_0^3a_1b_1^2-3a_0^2a_1^2b_1^2+21a_0a_1^3b_1^2|
|      -----------------------------------------------------------------------|
|      -9a_1^4b_1^2 3a_0^4b_0^2+20a_0^3a_1b_0^2+24a_0^2a_1^2b_0^2+4a_0a_1^3b_0|
|      -----------------------------------------------------------------------|
|      ^2-41a_1^4b_0^2-16a_0^4b_0b_1+a_0^3a_1b_0b_1+22a_0^2a_1^2b_0b_1+17a_0a_|
|      -----------------------------------------------------------------------|
|      1^3b_0b_1+3a_1^4b_0b_1-20a_0^4b_1^2-50a_0^3a_1b_1^2-46a_0^2a_1^2b_1^2- |
|      -----------------------------------------------------------------------|
|      27a_0a_1^3b_1^2+5a_1^4b_1^2                                            |
|      -----------------------------------------------------------------------|
|      -17a_0^3a_1b_0^2+9a_0^2a_1^2b_0^2-33a_0a_1^3b_0^2-8a_1^4b_0^2-28a_0^4b_|
|      -----------------------------------------------------------------------|
|      0b_1+7a_0^3a_1b_0b_1-32a_0^2a_1^2b_0b_1+39a_0a_1^3b_0b_1+36a_1^4b_0b_1+|
|      -----------------------------------------------------------------------|
|      17a_0^4b_1^2-12a_0^3a_1b_1^2+4a_0^2a_1^2b_1^2+40a_0a_1^3b_1^2+16a_1^4b_|
|      -----------------------------------------------------------------------|
|      1^2 9a_0^3a_1b_0^2-39a_0^2a_1^2b_0^2-37a_0a_1^3b_0^2-50a_1^4b_0^2+48a_0|
|      -----------------------------------------------------------------------|
|      ^4b_0b_1+20a_0^3a_1b_0b_1-a_0^2a_1^2b_0b_1-33a_0a_1^3b_0b_1-38a_1^4b_0b|
|      -----------------------------------------------------------------------|
|      _1+22a_0^4b_1^2+50a_0^3a_1b_1^2-4a_0^2a_1^2b_1^2+16a_0a_1^3b_1^2-37a_1^|
|      -----------------------------------------------------------------------|
|      4b_1^2 3a_0^4a_1b_0+20a_0^3a_1^2b_0+24a_0^2a_1^3b_0+4a_0a_1^4b_0-32a_0^|
|      -----------------------------------------------------------------------|
|      4a_1b_1+14a_0^3a_1^2b_1+3a_0^2a_1^3b_1+43a_0a_1^4b_1                   |
|      -----------------------------------------------------------------------|
|      -17a_0^3a_1^2b_0+9a_0^2a_1^3b_0-33a_0a_1^4b_0+3a_0^4a_1b_1+32a_0^3a_1^ |
|      -----------------------------------------------------------------------|
|      2b_1-48a_0^2a_1^3b_1-11a_0a_1^4b_1                                     |
|      -----------------------------------------------------------------------|
|      9a_0^3a_1^2b_0-39a_0^2a_1^3b_0-37a_0a_1^4b_0+44a_0^4a_1b_1+16a_0^3a_1^ |
|      -----------------------------------------------------------------------|
|      2b_1-7a_0^2a_1^3b_1+4a_0a_1^4b_1 3a_0^4a_1^2+20a_0^3a_1^3+24a_0^2a_1^4 |
|      -----------------------------------------------------------------------|
|      -17a_0^3a_1^3+9a_0^2a_1^4 9a_0^3a_1^3-39a_0^2a_1^4 |                   |
|                                                                             |
|o11 : Matrix                                                                 |
|-----------------------------------------------------------------------------|
|X(-2,-3))                                                                    |
+-----------------------------------------------------------------------------+
|i12 : basis({0,0}, image E^1 .dd_{1,-2})  -- image 2-dimensional             |
|                                                                             |
|o12 = {-11, 0}  | 0               0               |                          |
|      {-1, -10} | 0               0               |                          |
|      {-8, -1}  | 0               0               |                          |
|      {-8, -1}  | 0               0               |                          |
|      {-8, -1}  | 0               0               |                          |
|      {-7, -2}  | 0               0               |                          |
|      {-7, -2}  | 0               0               |                          |
|      {-7, -2}  | 0               0               |                          |
|      {-6, -3}  | 0               0               |                          |
|      {-6, -3}  | 0               0               |                          |
|      {-6, -3}  | 0               0               |                          |
|      {-6, -3}  | 0               0               |                          |
|      {-5, -4}  | 0               0               |                          |
|      {-5, -4}  | 0               0               |                          |
|      {-5, -4}  | 0               0               |                          |
|      {-4, -5}  | 0               0               |                          |
|      {-4, -5}  | 0               0               |                          |
|      {-6, -3}  | 0               0               |                          |
|      {-6, -3}  | 0               0               |                          |
|      {-6, -3}  | 0               0               |                          |
|      {-5, -4}  | 0               0               |                          |
|      {-5, -4}  | 0               0               |                          |
|      {-5, -4}  | 0               0               |                          |
|      {-5, -4}  | 0               0               |                          |
|      {-4, -5}  | 0               0               |                          |
|      {-4, -5}  | 0               0               |                          |
|      {-4, -5}  | 0               0               |                          |
|      {-4, -5}  | 0               0               |                          |
|      {-4, -5}  | 0               0               |                          |
|      {-3, -6}  | 0               0               |                          |
|      {-3, -6}  | 0               0               |                          |
|      {-3, -6}  | 0               0               |                          |
|      {-2, -7}  | a_1^2b_0^4b_1^3 a_1^2b_0^3b_1^4 |                          |
|      {-2, -7}  | 0               0               |                          |
|      {-2, -7}  | 0               0               |                          |
|                                                                             |
|o12 : Matrix                                                                 |
+-----------------------------------------------------------------------------+
|i13 : basis({0,0}, ker E^1 .dd_{1,-2}) -- map is injective                   |
|                                                                             |
|o13 = 0                                                                      |
|                                                                             |
|o13 : Matrix                                                                 |
+-----------------------------------------------------------------------------+
|i14 : basis({0,0}, target E^1 .dd_{1,-2}) -- target 2-dimensional            |
|                                                                             |
|o14 = {-8, -7} | a_0^4a_1^4b_0^4b_1^3 a_0^4a_1^4b_0^3b_1^4 |                 |
|                                                                             |
|o14 : Matrix                                                                 |
+-----------------------------------------------------------------------------+
|i15 : basis({0,0}, source E^1 .dd_{1,-2}) -- source 2 dimensional            |
|                                                                             |
|o15 = {-11, 0}  | 0               0               |                          |
|      {-1, -10} | 0               0               |                          |
|      {-8, -1}  | 0               0               |                          |
|      {-8, -1}  | 0               0               |                          |
|      {-8, -1}  | 0               0               |                          |
|      {-7, -2}  | 0               0               |                          |
|      {-7, -2}  | 0               0               |                          |
|      {-7, -2}  | 0               0               |                          |
|      {-6, -3}  | 0               0               |                          |
|      {-6, -3}  | 0               0               |                          |
|      {-6, -3}  | 0               0               |                          |
|      {-6, -3}  | 0               0               |                          |
|      {-5, -4}  | 0               0               |                          |
|      {-5, -4}  | 0               0               |                          |
|      {-5, -4}  | 0               0               |                          |
|      {-4, -5}  | 0               0               |                          |
|      {-4, -5}  | 0               0               |                          |
|      {-6, -3}  | 0               0               |                          |
|      {-6, -3}  | 0               0               |                          |
|      {-6, -3}  | 0               0               |                          |
|      {-5, -4}  | 0               0               |                          |
|      {-5, -4}  | 0               0               |                          |
|      {-5, -4}  | 0               0               |                          |
|      {-5, -4}  | 0               0               |                          |
|      {-4, -5}  | 0               0               |                          |
|      {-4, -5}  | 0               0               |                          |
|      {-4, -5}  | 0               0               |                          |
|      {-4, -5}  | 0               0               |                          |
|      {-4, -5}  | 0               0               |                          |
|      {-3, -6}  | 0               0               |                          |
|      {-3, -6}  | 0               0               |                          |
|      {-3, -6}  | 0               0               |                          |
|      {-2, -7}  | a_1^2b_0^4b_1^3 a_1^2b_0^3b_1^4 |                          |
|      {-2, -7}  | 0               0               |                          |
|      {-2, -7}  | 0               0               |                          |
|                                                                             |
|o15 : Matrix                                                                 |
+-----------------------------------------------------------------------------+

An alternative way to compute the connecting morphism is

+-----------------------------------------------------------------+
|i16 : prune connectingMorphism(Hom(G, f), - 2) ;                 |
|                                                                 |
|o16 : Matrix                                                     |
+-----------------------------------------------------------------+
|i17 : prune connectingMorphism(Hom(G, f), - 2) == E^1 .dd_{1, -2}|
|                                                                 |
|o17 = true                                                       |
+-----------------------------------------------------------------+
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:1817:0.

Spectral sequences and hypercohomology calculations
***************************************************

If $\mathcal{F}$ is a coherent sheaf on a smooth toric variety $X$ then
multigraded commutative algebra can be used to compute the cohomology groups
$H^i(X, \mathcal{F})$.

Indeed if $B$ is the irrelevant ideal of $X$ then the cohomology group $H^i(X,
\mathcal{F})$ can be realized as the degree zero piece of the multigraded
module $Ext^i(B^{[l]}, F)$ for sufficiently large $l$; here $B^{[l]}$ denotes
the $l$th Frobenius power of $B$ and $F$ is any multigraded module whose
corresponding sheaf on $X$ is $\mathcal{F}$.

Given the fan of $X$ and $F$ a sufficiently large power of $l$ can be
determined effectively. We refer to sections 2 and 3 of the paper "Cohomology
on Toric Varieties and Local Cohomology with Monomial Supports" for more
details.

In this example, we consider the case that $X = \mathbb{P}^1 \times
\mathbb{P}^1$ and $F = \mathcal{O}_C(1,0)$ where $C$ is a general divisor of
type $(3,3)$ on $X$. In this setting, $H^0(C,F)$ and $H^1(C, F)$ are both
$2$-dimensional vector spaces.

We first make the multi-graded coordinate ring of $\mathbb{P}^1 \times
\mathbb{P}^1$, the irrelevant ideal, and a sufficentily high Frobenus power of
the irrelevant ideal needed for our calculations.  Also the complex $G$ below
is a resolution of the irrelevant ideal.

+-----------------------------------------------------------------------+
|i1 : R = ZZ/101[a_0..b_1, Degrees=>{2:{1,0},2:{0,1}}]; -- PP^1 x PP^1  |
+-----------------------------------------------------------------------+
|i2 : B = intersect(ideal(a_0,a_1),ideal(b_0,b_1)) ; -- irrelevant ideal|
|                                                                       |
|o2 : Ideal of R                                                        |
+-----------------------------------------------------------------------+
|i3 : B = B_*/(x -> x^5)//ideal ; -- Sufficentily high Frobenius power  |
|                                                                       |
|o3 : Ideal of R                                                        |
+-----------------------------------------------------------------------+
|i4 : G = res image gens B ;                                            |
+-----------------------------------------------------------------------+

We next make the ideal, denoted by $I$ below, of a general divisor of type
$(3,3)$ on $\mathbb{P}^1 \times \mathbb{P}^1$.  Also the chain complex $F$
below is a resolution of this ideal.

+-------------------------------------------------------+
|i5 : I = ideal random(R^1, R^{{-3,-3}}) ; -- ideal of C|
|                                                       |
|o5 : Ideal of R                                        |
+-------------------------------------------------------+
|i6 : F = res comodule I                                |
|                                                       |
|      1      1                                         |
|o6 = R  <-- R  <-- 0                                   |
|                                                       |
|     0      1      2                                   |
|                                                       |
|o6 : ChainComplex                                      |
+-------------------------------------------------------+

To use hypercohomology to compute the cohomology groups of the line bundle
$\mathcal{O}_C(1,0)$ on $C$ we twist the complex $F$ above by a line of ruling
and then make a filtered complex whose associated spectral sequence abuts to
the desired cohomology groups.

+-----------------------------------------------------------------------------+
|i7 : K = Hom(G , filteredComplex (F ** R^{{1,0}})) ; -- Twist F by a line of |
|-----------------------------------------------------------------------------|
|ruling and make filtered complex whose ss abuts to HH OO_C(1,0)              |
+-----------------------------------------------------------------------------+
|i8 : E = prune spectralSequence K ; --the spectral sequence degenerates on   |
|-----------------------------------------------------------------------------|
|the second page                                                              |
+-----------------------------------------------------------------------------+
|i9 : E^1                                                                     |
|                                                                             |
|     +-----------------------------------------------+-----------------------|
|     | 1                                             | 1                     |
|o9 = |R                                              |R                      |
|     |                                               |                       |
|     |{0, 0}                                         |{1, 0}                 |
|     +-----------------------------------------------+-----------------------|
|     |cokernel {-11, 0}  | a_1^5 a_0^5 0     0     | |cokernel {-8, 3} | a_1^|
|     |         {-1, -10} | 0     0     b_1^5 b_0^5 | |         {2, -7} | 0   |
|     |                                               |                       |
|     |{0, -1}                                        |{1, -1}                |
|     +-----------------------------------------------+-----------------------|
|     |cokernel {-11, -10} | b_1^5 b_0^5 a_1^5 a_0^5 ||cokernel {-8, -7} | b_1|
|     |                                               |                       |
|     |{0, -2}                                        |{1, -2}                |
|     +-----------------------------------------------+-----------------------|
|                                                                             |
|o9 : SpectralSequencePage                                                    |
|-----------------------------------------------------------------------------|
|----------------------+                                                      |
|                      |                                                      |
|                      |                                                      |
|                      |                                                      |
|                      |                                                      |
|----------------------+                                                      |
|5 a_0^5 0     0     | |                                                      |
|  0     b_1^5 b_0^5 | |                                                      |
|                      |                                                      |
|                      |                                                      |
|----------------------+                                                      |
|^5 b_0^5 a_1^5 a_0^5 ||                                                      |
|                      |                                                      |
|                      |                                                      |
|----------------------+                                                      |
+-----------------------------------------------------------------------------+
|i10 : E^2 ; -- output is a mess                                              |
+-----------------------------------------------------------------------------+

The cohomology groups we want are obtained as follows.

+----------------------------------------------------+
|i11 : basis({0,0}, E^2_{0,0}) --  == HH^0 OO_C(1,0) |
|                                                    |
|o11 = {-1, 0} | a_0 a_1 |                           |
|                                                    |
|o11 : Matrix                                        |
+----------------------------------------------------+
|i12 : basis({0,0}, E^2_{1,-2}) --  == HH^1 OO_C(1,0)|
|                                                    |
|o12 = {-8, -1} | 0               0               |  |
|      {-8, -1} | 0               0               |  |
|      {-8, -1} | 0               0               |  |
|      {-7, -2} | 0               0               |  |
|      {-7, -2} | 0               0               |  |
|      {-7, -2} | 0               0               |  |
|      {-6, -3} | 0               0               |  |
|      {-6, -3} | 0               0               |  |
|      {-6, -3} | 0               0               |  |
|      {-6, -3} | 0               0               |  |
|      {-5, -4} | 0               0               |  |
|      {-5, -4} | 0               0               |  |
|      {-5, -4} | 0               0               |  |
|      {-4, -5} | 0               0               |  |
|      {-4, -5} | 0               0               |  |
|      {-6, -3} | 0               0               |  |
|      {-6, -3} | 0               0               |  |
|      {-6, -3} | 0               0               |  |
|      {-5, -4} | 0               0               |  |
|      {-5, -4} | 0               0               |  |
|      {-5, -4} | 0               0               |  |
|      {-5, -4} | 0               0               |  |
|      {-4, -5} | 0               0               |  |
|      {-4, -5} | 0               0               |  |
|      {-4, -5} | 0               0               |  |
|      {-4, -5} | 0               0               |  |
|      {-4, -5} | 0               0               |  |
|      {-3, -6} | 0               0               |  |
|      {-3, -6} | 0               0               |  |
|      {-3, -6} | 0               0               |  |
|      {-2, -7} | 0               0               |  |
|      {-2, -7} | 0               0               |  |
|      {-2, -7} | a_1^2b_0^4b_1^3 a_1^2b_0^3b_1^4 |  |
|                                                    |
|o12 : Matrix                                        |
+----------------------------------------------------+

See also
========

  * Spectral sequences and connecting morphisms
  * Spectral sequences and non-Koszul syzygies
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:1889:0.

Spectral sequences and non-Koszul syzygies
******************************************

We illustrate some aspects of the paper "A case study in bigraded commutative
algebra" by Cox-Dickenstein-Schenck. In that paper, an appropriate term on the
E_2 page of a suitable spectral sequence corresponds to non-koszul syzygies.

Using our indexing conventions, the E^2_{3,-1} term will be what the
$E^{0,1}_2$ term is in their paper.

We illustrate an instance of the non-generic case for non-Koszul syzygies. To
do this we look at the three polynomials used in their Example 4.3. The
behaviour that we expect to exhibit is predicted by their Proposition 5.2.

+-----------------------------------------------------------------------------+
|i1 : R = QQ[x,y,z,w, Degrees => {{1,0},{1,0},{0,1},{0,1}}];                  |
+-----------------------------------------------------------------------------+
|i2 : B = ideal(x*z, x*w, y*z, y*w);                                          |
|                                                                             |
|o2 : Ideal of R                                                              |
+-----------------------------------------------------------------------------+
|i3 : p_0 = x^2*z;                                                            |
+-----------------------------------------------------------------------------+
|i4 : p_1 = y^2*w;                                                            |
+-----------------------------------------------------------------------------+
|i5 : p_2 = y^2*z+x^2*w;                                                      |
+-----------------------------------------------------------------------------+
|i6 : I = ideal(p_0,p_1,p_2);                                                 |
|                                                                             |
|o6 : Ideal of R                                                              |
+-----------------------------------------------------------------------------+
|i7 : B = B_*/(x -> x^2)//ideal;                                              |
|                                                                             |
|o7 : Ideal of R                                                              |
+-----------------------------------------------------------------------------+
|i8 : G = complete res image gens B;                                          |
+-----------------------------------------------------------------------------+
|i9 : F = koszul gens I;                                                      |
+-----------------------------------------------------------------------------+
|i10 : K = Hom(G, filteredComplex(F));                                        |
+-----------------------------------------------------------------------------+
|i11 : E = prune spectralSequence K;                                          |
+-----------------------------------------------------------------------------+
|i12 : E^1                                                                    |
|                                                                             |
|      +---------------------------------+------------------------------------|
|      | 1                               | 3                                  |
|o12 = |R                                |R                                   |
|      |                                 |                                    |
|      |{0, 0}                           |{1, 0}                              |
|      +---------------------------------+------------------------------------|
|      |cokernel {-4, 0} | y2 x2 0  0  | |cokernel {-2, 1} | y2 x2 0  0  0  0 |
|      |         {0, -4} | 0  0  w2 z2 | |         {-2, 1} | 0  0  y2 x2 0  0 |
|      |                                 |         {-2, 1} | 0  0  0  0  y2 x2|
|      |{0, -1}                          |         {2, -3} | 0  0  0  0  0  0 |
|      |                                 |         {2, -3} | 0  0  0  0  0  0 |
|      |                                 |         {2, -3} | 0  0  0  0  0  0 |
|      |                                 |                                    |
|      |                                 |{1, -1}                             |
|      +---------------------------------+------------------------------------|
|      |cokernel {-4, -4} | w2 z2 y2 x2 ||cokernel {-2, -3} | w2 z2 y2 x2 0  0|
|      |                                 |         {-2, -3} | 0  0  0  0  w2 z|
|      |{0, -2}                          |         {-2, -3} | 0  0  0  0  0  0|
|      |                                 |                                    |
|      |                                 |{1, -2}                             |
|      +---------------------------------+------------------------------------|
|                                                                             |
|o12 : SpectralSequencePage                                                   |
|-----------------------------------------------------------------------------|
|---------------------+-------------------------------------------------------|
|                     | 3                                                     |
|                     |R                                                      |
|                     |                                                       |
|                     |{2, 0}                                                 |
|---------------------+-------------------------------------------------------|
| 0  0  0  0  0  0  | |cokernel {0, 2}  | y2 x2 0  0  0  0  0  0  0  0  0  0  |
| 0  0  0  0  0  0  | |         {0, 2}  | 0  0  y2 x2 0  0  0  0  0  0  0  0  |
| 0  0  0  0  0  0  | |         {0, 2}  | 0  0  0  0  y2 x2 0  0  0  0  0  0  |
| w2 z2 0  0  0  0  | |         {4, -2} | 0  0  0  0  0  0  w2 z2 0  0  0  0  |
| 0  0  w2 z2 0  0  | |         {4, -2} | 0  0  0  0  0  0  0  0  w2 z2 0  0  |
| 0  0  0  0  w2 z2 | |         {4, -2} | 0  0  0  0  0  0  0  0  0  0  w2 z2 |
|                     |                                                       |
|                     |{2, -1}                                                |
|---------------------+-------------------------------------------------------|
|  0  0  0  0  0  0  ||cokernel {0, -2} | w2 z2 y2 x2 0  0  0  0  0  0  0  0  |
|2 y2 x2 0  0  0  0  ||         {0, -2} | 0  0  0  0  w2 z2 y2 x2 0  0  0  0  |
|  0  0  w2 z2 y2 x2 ||         {0, -2} | 0  0  0  0  0  0  0  0  w2 z2 y2 x2 |
|                     |                                                       |
|                     |{2, -2}                                                |
|---------------------+-------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-+--------------------------------+                                          |
| | 1                              |                                          |
| |R                               |                                          |
| |                                |                                          |
| |{3, 0}                          |                                          |
|-+--------------------------------+                                          |
|||cokernel {2, 3}  | y2 x2 0  0  ||                                          |
|||         {6, -1} | 0  0  w2 z2 ||                                          |
|||                                |                                          |
|||{3, -1}                         |                                          |
|||                                |                                          |
|||                                |                                          |
| |                                |                                          |
| |                                |                                          |
|-+--------------------------------+                                          |
|||cokernel {2, -1} | w2 z2 y2 x2 ||                                          |
|||                                |                                          |
|||{3, -2}                         |                                          |
| |                                |                                          |
| |                                |                                          |
|-+--------------------------------+                                          |
+-----------------------------------------------------------------------------+
|i13 : E^2                                                                    |
|                                                                             |
|      +------------------------------------------------+---------------------|
|o13 = |cokernel | y2w y2z+x2w x2z |                    |cokernel {2, 3} | y2 |
|      |                                                |         {6, 1} | 0  |
|      |{0, 0}                                          |                     |
|      |                                                |{1, 0}               |
|      +------------------------------------------------+---------------------|
|      |cokernel {-4, 0} | y2 x2 0  0  0   0       0   ||cokernel {-2, 1} | y2|
|      |         {0, -4} | 0  0  w2 z2 y2w y2z+x2w x2z ||         {-2, 1} | 0 |
|      |                                                |         {-2, 1} | 0 |
|      |{0, -1}                                         |         {2, -2} | 0 |
|      |                                                |         {2, -2} | 0 |
|      |                                                |         {2, -2} | 0 |
|      |                                                |         {2, -2} | 0 |
|      |                                                |         {6, -3} | 0 |
|      |                                                |                     |
|      |                                                |{1, -1}              |
|      +------------------------------------------------+---------------------|
|      |cokernel {-4, -4} | w2 z2 y2 x2 |               |cokernel {-2, -3} | w|
|      |                                                |         {-2, -3} | 0|
|      |{0, -2}                                         |         {-2, -3} | 0|
|      |                                                |                     |
|      |                                                |{1, -2}              |
|      +------------------------------------------------+---------------------|
|                                                                             |
|o13 : SpectralSequencePage                                                   |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------+-----------------------|
|x2 0 0 |                                             |0                      |
|0  w z |                                             |                       |
|                                                     |{2, 0}                 |
|                                                     |                       |
|-----------------------------------------------------+-----------------------|
| x2 0  0  0  0  0 0 0 0 0 0  0   0  0   0   0   0 0 ||cokernel {0, 2}  | y2 x|
| 0  y2 x2 0  0  0 0 0 0 0 0  0   0  0   0   0   0 0 ||         {0, 2}  | 0  0|
| 0  0  0  y2 x2 0 0 0 0 0 0  0   0  0   0   0   0 0 ||         {0, 2}  | 0  0|
| 0  0  0  0  0  z 0 0 0 w w2 0   0  -y2 y2w 0   0 0 ||         {4, 0}  | 0  0|
| 0  0  0  0  0  0 w z 0 0 0  x2  0  0   0   0   0 0 ||         {4, 0}  | 0  0|
| 0  0  0  0  0  0 0 w z 0 0  -y2 0  0   0   0   0 0 ||         {4, 0}  | 0  0|
| 0  0  0  0  0  0 0 0 w z 0  0   w2 x2  0   y2w 0 0 ||         {6, -1} | 0  0|
| 0  0  0  0  0  0 0 0 0 0 0  0   0  0   0   0   w z ||         {6, -1} | 0  0|
|                                                     |                       |
|                                                     |{2, -1}                |
|-----------------------------------------------------+-----------------------|
|2 z2 y2 x2 0  0  0  0  0  0  0  0  |                 |cokernel {0, -2} | w2 z|
|  0  0  0  w2 z2 y2 x2 0  0  0  0  |                 |         {0, -2} | 0  0|
|  0  0  0  0  0  0  0  w2 z2 y2 x2 |                 |         {0, -2} | 0  0|
|                                                     |                       |
|                                                     |{2, -2}                |
|-----------------------------------------------------+-----------------------|
|-----------------------------------------------------------------------------|
|-------------------------------------------+--------------------------------+|
|                                           |0                               ||
|                                           |                                ||
|                                           |{3, 0}                          ||
|                                           |                                ||
|-------------------------------------------+--------------------------------+|
|2 0  0  0  0  0 0 0 0 0 0 0   0   0 0 0 0 ||cokernel {2, 3} | y2 x2 0 0 |   ||
|  y2 x2 0  0  0 0 0 0 0 0 0   0   0 0 0 0 ||         {6, 1} | 0  0  w z |   ||
|  0  0  y2 x2 0 0 0 0 0 0 0   0   0 0 0 0 ||                                ||
|  0  0  0  0  w z 0 0 0 0 x2  -y2 0 0 0 0 ||{3, -1}                         ||
|  0  0  0  0  0 0 w z 0 0 -y2 0   0 0 0 0 ||                                ||
|  0  0  0  0  0 0 0 0 w z 0   x2  0 0 0 0 ||                                ||
|  0  0  0  0  0 0 0 0 0 0 0   0   w z 0 0 ||                                ||
|  0  0  0  0  0 0 0 0 0 0 0   0   0 0 w z ||                                ||
|                                           |                                ||
|                                           |                                ||
|-------------------------------------------+--------------------------------+|
|2 y2 x2 0  0  0  0  0  0  0  0  |          |cokernel {2, -1} | w2 z2 y2 x2 |||
|  0  0  w2 z2 y2 x2 0  0  0  0  |          |                                ||
|  0  0  0  0  0  0  w2 z2 y2 x2 |          |{3, -2}                         ||
|                                           |                                ||
|                                           |                                ||
|-------------------------------------------+--------------------------------+|
+-----------------------------------------------------------------------------+

The degree zero piece of the module $E^2_{3,-1}$ twisted by $R((2,3))$ below
shows that there is a $1$-dimensional space of non-Koszul syzygies of bi-degree
$(2,3)$.  This is what is predicted by the paper.

+-----------------------------------------------------+
|i14 : E^2_{3,-1}                                     |
|                                                     |
|o14 = cokernel {2, 3} | y2 x2 0 0 |                  |
|               {6, 1} | 0  0  w z |                  |
|                                                     |
|                             2                       |
|o14 : R-module, quotient of R                        |
+-----------------------------------------------------+
|i15 : basis({0,0}, E^2_{3, -1} ** R^{{2, 3}})        |
|                                                     |
|o15 = {0, 0}  | 1 |                                  |
|      {4, -2} | 0 |                                  |
|                                                     |
|o15 : Matrix                                         |
+-----------------------------------------------------+
|i16 : E^2 .dd_{3, -1}                                |
|                                                     |
|o16 = {2, 3} | -1 0 |                                |
|      {6, 1} | 0  1 |                                |
|                                                     |
|o16 : Matrix                                         |
+-----------------------------------------------------+
|i17 : basis({0,0}, image E^2 .dd_{3,-1} ** R^{{2,3}})|
|                                                     |
|o17 = {0, 0}  | 1 |                                  |
|      {4, -2} | 0 |                                  |
|                                                     |
|o17 : Matrix                                         |
+-----------------------------------------------------+
|i18 : basis({0,0}, E^2_{1,0} ** R^{{2,3}})           |
|                                                     |
|o18 = {0, 0}  | 1 |                                  |
|      {4, -2} | 0 |                                  |
|                                                     |
|o18 : Matrix                                         |
+-----------------------------------------------------+

The degree zero piece of the module $E^2_{3,-1}$ twisted by $R((6,1))$ below
shows that there is a $1$-dimensional space of non-Koszul syzygies of bi-degree
$(6,1)$.  This is also what is predicted by the paper.

+---------------------------------------------+
|i19 : basis({0,0}, E^2 _{3, -1} ** R^{{6,1}})|
|                                             |
|o19 = {-4, 2} | 0 |                          |
|      {0, 0}  | 1 |                          |
|                                             |
|o19 : Matrix                                 |
+---------------------------------------------+
|i20 : isIsomorphism(E^2 .dd_{3, -1})         |
|                                             |
|o20 = true                                   |
+---------------------------------------------+
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:1766:0.

SpectralSequence -- the type of all spectral sequences
******************************************************

Description
===========

A (homological, or lower index) spectral sequence consists of:

1. A sequence of modules $\{E^r_{p,q}\}$ for $p,q \in \mathbb{Z}$ and $r \geq
0$;

2. A collection of homomorphisms $\{d^r_{p,q}: E^r_{p,q} \rightarrow
E^r_{p-r,q+r-1} \}$, for $p,q \in \mathbb{Z}$ and $ r \geq 0$, such that
$d^r_{p,q} d^r_{p+r,q-r+1} = 0$ ;

3. A collection of isomorphisms $E^{r+1}_{p,q}  \rightarrow  ker d^r_{p,q} /
image d^r_{p+r,q-r+1}$.

Alternatively a (cohomological, or upper index) spectral sequence consists of:

1'. A sequence of modules $\{E_r^{p,q}\}$ for $p,q \in \mathbb{Z}$, and $r \geq
0$;

2'. A collection of homomorphisms $\{d_r^{p,q}: E_r^{p,q} \rightarrow
E_{r}^{p+r,q-r+1}\}$ for $p,q \in \mathbb{Z}, r \geq 0$ such that $d_r^{p,q}
d_r^{p-r,q+r-1} = 0$ ;

3'. A collection of isomorphisms $E_{r+1}^{p,q}  $\rightarrow$ ker d_r^{p,q} /
image d_r^{p-r,q+r-1}$.

The type SpectralSequence is a data type for working with spectral sequences.
In this package, a spectral sequence is represented by a sequence of spectral
sequence pages.

Caveat
======

All spectral sequences arise from bounded filtrations of bounded chain
complexes.  Ascending filtrations of degree $-1$ chain complexes determine
spectral sequences of the first type.  Descending filtrations of degree $1$
chain complex determine spectral sequences of the second type.

See also
========

  * SpectralSequencePage -- the type of all
    spectral sequence pages
  * SpectralSequencePageMap -- the type of all
    spectral sequence page maps
  * Filtered complexes and simplicial complexes
  * Filtrations and tensor product complexes
  * Filtrations and homomorphism complexes

Functions and methods returning a spectral sequence:
====================================================

  * minimalPresentation(SpectralSequence)
    -- a minimal presentation of a
    spectral sequence
  * "prune(SpectralSequence)" -- see
    minimalPresentation(SpectralSequence),
    -- a minimal presentation of a
    spectral sequence
  * spectralSequence(FilteredComplex)
    -- construct a spectral sequence
    from a filtered complex

Methods that use a spectral sequence:
=====================================

  * chainComplex(SpectralSequence),
    -- the underlying chain complex of a Spectral Sequence
  * describe(SpectralSequence) -- real
    description
  * "edgeComplex(SpectralSequence)" -- see edgeComplex, --
    the edge homomorphisms
  * expression(SpectralSequence)
  * filteredComplex(SpectralSequence)
    -- obtain the filtered complex
    associated to the spectral sequence
  * homologyIsomorphism(SpectralSequence,ZZ,ZZ,ZZ)
    -- the homology
    isomorphism
  * net(SpectralSequence)
  * SpectralSequence ^ InfiniteNumber,
    -- the infinity page of a spectral sequence
  * "SpectralSequence _ InfiniteNumber" -- see SpectralSequence ^ InfiniteNumber,
    -- the infinity page of
    a spectral sequence
  * SpectralSequence ^ ZZ -- the kth page of a
    spectral sequence
  * SpectralSequence _ ZZ -- the kth page of a
    spectral sequence

For the programmer
==================

The object SpectralSequence, is a type (Macaulay2Doc),
with ancestor classes MutableHashTable (Macaulay2Doc),
< HashTable (Macaulay2Doc) <
Thing (Macaulay2Doc).

-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2179:0.

spectralSequence -- construct a spectral sequence
*************************************************

  * Usage:
        E = spectralSequence K
  * Inputs:
      * K, a filtered chain complex, A filtered complex
  * Optional inputs (Macaulay2Doc),:
      * Prune, =>
        ..., default value false,
  * Outputs:
      * E, a spectral sequence,

Description
===========

This is the primitive spectral sequence constructor.

In the example below we construct a spectral sequence $E$ from the filtered
complex $K$.

+----------------------------------------------------+
|i1 : B = QQ[a..d];                                  |
+----------------------------------------------------+
|i2 : J = ideal vars B;                              |
|                                                    |
|o2 : Ideal of B                                     |
+----------------------------------------------------+
|i3 : C = complete res monomialCurveIdeal(B,{1,3,4});|
+----------------------------------------------------+
|i4 : K = filteredComplex(J,C,4);                    |
+----------------------------------------------------+
|i5 : E = spectralSequence K                         |
|                                                    |
|o5 = E                                              |
|                                                    |
|o5 : SpectralSequence                               |
+----------------------------------------------------+

To view pages and or maps we proceed, for example, as follows (note we suppress
the output of the E^0.dd command to prevent excessive output)

+-----------------------------------------------------------------------------+
|i6 : E^0                                                                     |
|                                                                             |
|     +-----------------------------------------------------------------------|
|o6 = |image | a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab2d abc2|
|     |                                                                       |
|     |{-4, 4}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 3}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 2}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 1}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 0}                                                                |
|     +-----------------------------------------------------------------------|
|                                                                             |
|o6 : SpectralSequencePage                                                    |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 bd3 c4 c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|--------------------------+--------------------------------------------------|
|3d c2d2 cd3 d4 0 0 0 0 0 ||subquotient ({2} | a3 0  0  0  a2b 0   0   0   a2c|
|                          |             {3} | 0  a3 0  0  0   a2b 0   0   0  |
|                          |             {3} | 0  0  a3 0  0   0   a2b 0   0  |
|                          |             {3} | 0  0  0  a3 0   0   0   a2b 0  |
|                          |                                                  |
|                          |{-3, 4}                                           |
|--------------------------+--------------------------------------------------|
|                          |subquotient (| a3 a2b a2c a2d ab2 abc abd ac2 acd |
|                          |                                                  |
|                          |{-3, 3}                                           |
|                          |                                                  |
|                          |                                                  |
|                          |                                                  |
|--------------------------+--------------------------------------------------|
|                          |0                                                 |
|                          |                                                  |
|                          |{-3, 2}                                           |
|                          |                                                  |
|                          |                                                  |
|                          |                                                  |
|--------------------------+--------------------------------------------------|
|                          |0                                                 |
|                          |                                                  |
|                          |{-3, 1}                                           |
|                          |                                                  |
|                          |                                                  |
|                          |                                                  |
|--------------------------+--------------------------------------------------|
|                          |0                                                 |
|                          |                                                  |
|                          |{-3, 0}                                           |
|--------------------------+--------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   |
| a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   |
| 0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   |
| 0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|ad2 b3 b2c b2d bc2 bcd bd2 c3 c2d cd2 d3 a4bc-a5d a4b3-a6c a5c2-a4b2d a4c3-a4|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|ac2 0   0   0   acd 0   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b|
|0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0|
|0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0|
|0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bd2 a3b2c-a4bd a3b4-a5bc a4bc2-a3b3d a3bc3-a3b2d2 a3bc2-a4cd a3b3c-a5c2 a4c3-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2|
|   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0 |
|   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0 |
|   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a3b2cd a3c4-a3bcd2 a3bcd-a4d2 a3b3d-a5cd a4c2d-a3b2d2 a3c3d-a3bd3 a2b3c-a3b2d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d 0   0   0   cd2 0   0   0   d3 0  0  0  -a4b2 -a5c -a4bd -a4c2 -a3b3 -a4bc |
|  c2d 0   0   0   cd2 0   0   0  d3 0  0  a4c   a4d  0     0     a3bc  a3bd  |
|  0   c2d 0   0   0   cd2 0   0  0  d3 0  a5    a4b  -a4c  -a4d  a4b   a3b2  |
|  0   0   c2d 0   0   0   cd2 0  0  0  d3 0     0    a5    a4b   0     0     |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| a2b5-a4b2c a3b2c2-a2b4d a2b2c3-a2b3d2 a2b2c2-a3bcd a2b4c-a4bc2 a3bc3-a2b3cd |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-a3b2d -a3bc2 -a3b2c -a4c2 -a3bcd -a3c3 -a3b2d -a4cd -a3bd2 -a3c2d -a2b4 -a3b|
|0      0      a3c2   a3cd  0      0     a3cd   a3d2  0      0      a2b2c a2b2|
|-a3bc  -a3bd  a4c    a3bc  -a3c2  -a3cd a4d    a3bd  -a3cd  -a3d2  a3b2  a2b3|
|a4b    a3b2   0      0     a4c    a3bc  0      0     a4d    a3bd   0     0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a2bc4-a2b2cd2 a2b2cd-a3bd2 a2b4d-a4bcd a3bc2d-a2b3d2 a2bc3d-a2b2d3 a2bc3-a3c2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2c -a2b3d -a2b2c2 -a2b3c -a3bc2 -a2b2cd -a2bc3 -a2b3d -a3bcd -a2b2d2 -a2bc2d |
|d  0      0       a2bc2  a2bcd  0       0      a2bcd  a2bd2  0       0       |
|   -a2b2c -a2b2d  a3bc   a2b2c  -a2bc2  -a2bcd a3bd   a2b2d  -a2bcd  -a2bd2  |
|   a3b2   a2b3    0      0      a3bc    a2b2c  0      0      a3bd    a2b2d   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d a2b3c2-a4c3 a3c4-a2b2c2d a2c5-a2bc2d2 a2bc2d-a3cd2 a2b3cd-a4c2d a3c3d-a2b2c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-a2b2c2 -a3c3 -a2bc2d -a2c4  -a2b2cd -a3c2d -a2bcd2 -a2c3d -a2b2d2 -a3cd2 -a2|
|a2c3    a2c2d 0       0      a2c2d   a2cd2  0       0      a2cd2   a2d3   0  |
|a3c2    a2bc2 -a2c3   -a2c2d a3cd    a2bcd  -a2c2d  -a2cd2 a3d2    a2bd2  -a2|
|0       0     a3c2    a2bc2  0       0      a3cd    a2bcd  0       0      a3d|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2 a2c4d-a2bcd3 a2bcd2-a3d3 a2b3d2-a4cd2 a3c2d2-a2b2d3 a2c3d2-a2bd4 ab4c-a2b3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|bd3 -a2c2d2 -ab5 -a2b3c -ab4d -ab3c2 -ab4c -a2b2c2 -ab3cd -ab2c3 -ab4d -a2b2c|
|    0       ab3c ab3d   0     0      ab2c2 ab2cd   0      0      ab2cd ab2d2 |
|cd2 -a2d3   a2b3 ab4    -ab3c -ab3d  a2b2c ab3c    -ab2c2 -ab2cd a2b2d ab3d  |
|2   a2bd2   0    0      a2b3  ab4    0     0       a2b2c  ab3c   0     0     |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d ab6-a3b3c a2b3c2-ab5d ab3c3-ab4d2 ab3c2-a2b2cd ab5c-a3b2c2 a2b2c3-ab4cd ab2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d -ab3d2 -ab2c2d -ab3c2 -a2bc3 -ab2c2d -abc4  -ab3cd -a2bc2d -ab2cd2 -abc3d -|
|  0      0       abc3   abc2d  0       0      abc2d  abcd2   0       0      a|
|  -ab2cd -ab2d2  a2bc2  ab2c2  -abc3   -abc2d a2bcd  ab2cd   -abc2d  -abcd2 a|
|  a2b2d  ab3d    0      0      a2bc2   ab2c2  0      0       a2bcd   ab2cd  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c4-ab3cd2 ab3cd-a2b2d2 ab5d-a3b2cd a2b2c2d-ab4d2 ab2c3d-ab3d3 ab2c3-a2bc2d ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|ab3d2 -a2bcd2 -ab2d3 -abc2d2 -ab2c3 -a2c4 -abc3d -ac5  -ab2c2d -a2c3d -abc2d2|
|bcd2  abd3    0      0       ac4    ac3d  0      0     ac3d    ac2d2  0      |
|2bd2  ab2d2   -abcd2 -abd3   a2c3   abc3  -ac4   -ac3d a2c2d   abc2d  -ac3d  |
|      0       a2bd2  ab2d2   0      0     a2c3   abc3  0       0      a2c2d  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|4c2-a3bc3 a2bc4-ab3c2d abc5-ab2c2d2 ab2c2d-a2bcd2 ab4cd-a3bc2d a2bc3d-ab3cd2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| -ac4d  -ab2cd2 -a2c2d2 -abcd3 -ac3d2 -ab2d3 -a2cd3 -abd4 -ac2d3 -b6 -ab4c -b|
| 0      ac2d2   acd3    0      0      acd3   ad4    0     0      b4c b4d   0 |
| -ac2d2 a2cd2   abcd2   -ac2d2 -acd3  a2d3   abd3   -acd3 -ad4   ab4 b5    -b|
| abc2d  0       0       a2cd2  abcd2  0      0      a2d3  abd3   0   0     ab|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|abc4d-ab2cd3 ab2cd2-a2bd3 ab4d2-a3bcd2 a2bc2d2-ab3d3 abc3d2-ab2d4 abc4-a2c3d |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|5d -b4c2 -b5c -ab3c2 -b4cd -b3c3 -b5d -ab3cd -b4d2 -b3c2d -b4c2 -ab2c3 -b3c2d|
|   0     b3c2 b3cd   0     0     b3cd b3d2   0     0      b2c3  b2c2d  0     |
|4c -b4d  ab3c b4c    -b3c2 -b3cd ab3d b4d    -b3cd -b3d2  ab2c2 b3c2   -b2c3 |
|4  b5    0    0      ab3c  b4c   0    0      ab3d  b4d    0     0      ab2c2 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|ab3c3-a3c4 a2c5-ab2c3d ac6-abc3d2 abc3d-a2c2d2 ab3c2d-a3c3d a2c4d-ab2c2d2 ac5|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| -b2c4  -b4cd -ab2c2d -b3cd2 -b2c3d -b4d2 -ab2cd2 -b3d3  -b2c2d2 -b3c3 -abc4 |
| 0      b2c2d b2cd2   0      0      b2cd2 b2d3    0      0       bc4   bc3d  |
| -b2c2d ab2cd b3cd    -b2c2d -b2cd2 ab2d2 b3d2    -b2cd2 -b2d3   abc3  b2c3  |
| b3c2   0     0       ab2cd  b3cd   0     0       ab2d2  b3d2    0     0     |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d-abc2d3 abc2d2-a2cd3 ab3cd2-a3c2d2 a2c3d2-ab2cd3 ac4d2-abcd4 abcd3-a2d4 ab3d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-b2c3d -bc5  -b3c2d -abc3d -b2c2d2 -bc4d  -b3cd2 -abc2d2 -b2cd3 -bc3d2 -b3d3 |
|0      0     bc3d   bc2d2  0       0      bc2d2  bcd3    0      0      bcd3  |
|-bc4   -bc3d abc2d  b2c2d  -bc3d   -bc2d2 abcd2  b2cd2   -bc2d2 -bcd3  abd3  |
|abc3   b2c3  0      0      abc2d   b2c2d  0      0       abcd2  b2cd2  0     |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3-a3cd3 a2c2d3-ab2d4 ac3d3-abd5 b5c-ab4d b7-a2b4c ab4c2-b6d b4c3-b5d2 b4c2-ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-abcd3 -b2d4 -bc2d3 -b2c4 -ac5 -bc4d -c6  -b2c3d -ac4d -bc3d2 -c5d  -b2c2d2 -|
|bd4    0     0      c5    c4d  0     0    c4d    c3d2  0      0     c3d2    c|
|b2d3   -bcd3 -bd4   ac4   bc4  -c5   -c4d ac3d   bc3d  -c4d   -c3d2 ac2d2   b|
|0      abd3  b2d3   0     0    ac4   bc4  0      0     ac3d   bc3d  0       0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3cd b6c-a2b3c2 ab3c3-b5cd b3c4-b4cd2 b4cd-ab3d2 b6d-a2b3cd ab3c2d-b5d2 b3c3d-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|ac3d2 -bc2d3 -c4d2 -b2cd3 -ac2d3 -bcd4 -c3d3 -b2d4 -acd4 -bd5 -c2d4 a4 0  0  |
|2d3   0      0     c2d3   cd4    0     0     cd4   d5    0    0     0  a4 0  |
|c2d2  -c3d2  -c2d3 acd3   bcd3   -c2d3 -cd4  ad4   bd4   -cd4 -d5   0  0  a4 |
|      ac2d2  bc2d2 0      0      acd3  bcd3  0     0     ad4  bd4   0  0  0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b4d3 b3c3-ab2c2d b5c2-a2b2c3 ab2c4-b4c2d b2c5-b3c2d2 b3c2d-ab2cd2 b5cd-a2b2c2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0  a3b 0   0   0   a3c 0   0   0   a3d 0   0   0   a2b2 0    0    0    a2bc 0|
|0  0   a3b 0   0   0   a3c 0   0   0   a3d 0   0   0    a2b2 0    0    0    a|
|0  0   0   a3b 0   0   0   a3c 0   0   0   a3d 0   0    0    a2b2 0    0    0|
|a4 0   0   0   a3b 0   0   0   a3c 0   0   0   a3d 0    0    0    a2b2 0    0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d ab2c3d-b4cd2 b2c4d-b3cd3 b3cd2-ab2d3 b5d2-a2b2cd2 ab2c2d2-b4d3 b2c3d2-b3d4 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d|
|2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0  |
|    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0  |
|    0    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b2c4-abc3d b4c3-a2bc4 abc5-b3c3d bc6-b2c3d2 b2c3d-abc2d2 b4c2d-a2bc3d abc4d-b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2 0    0    0    ab3 0   0   0   ab2c 0    0    0    ab2d 0    0    0    abc2|
|  a2d2 0    0    0   ab3 0   0   0    ab2c 0    0    0    ab2d 0    0    0   |
|  0    a2d2 0    0   0   ab3 0   0    0    ab2c 0    0    0    ab2d 0    0   |
|  0    0    a2d2 0   0   0   ab3 0    0    0    ab2c 0    0    0    ab2d 0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3c2d2 bc5d-b2c2d3 b2c2d2-abcd3 b4cd2-a2bc2d2 abc3d2-b3cd3 bc4d2-b2cd4 b2cd3-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0    0    0    abcd 0    0    0    abd2 0    0    0    ac3 0   0   0   ac2d |
| abc2 0    0    0    abcd 0    0    0    abd2 0    0    0   ac3 0   0   0    |
| 0    abc2 0    0    0    abcd 0    0    0    abd2 0    0   0   ac3 0   0    |
| 0    0    abc2 0    0    0    abcd 0    0    0    abd2 0   0   0   ac3 0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bd4 b4d3-a2bcd3 abc2d3-b3d4 bc3d3-b2d5 bc5-ac4d b3c4-a2c5 ac6-b2c4d c7-bc4d2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0    0    0    acd2 0    0    0    ad3 0   0   0   b4 0  0  0  b3c 0   0   0 |
|ac2d 0    0    0    acd2 0    0    0   ad3 0   0   0  b4 0  0  0   b3c 0   0 |
|0    ac2d 0    0    0    acd2 0    0   0   ad3 0   0  0  b4 0  0   0   b3c 0 |
|0    0    ac2d 0    0    0    acd2 0   0   0   ad3 0  0  0  b4 0   0   0   b3|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bc4d-ac3d2 b3c3d-a2c4d ac5d-b2c3d2 c6d-bc3d3 bc3d2-ac2d3 b3c2d2-a2c3d2 ac4d2-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  b3d 0   0   0   b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0   |
|  0   b3d 0   0   0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0   |
|  0   0   b3d 0   0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0   |
|c 0   0   0   b3d 0    0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b2c2d3 c5d2-bc2d4 bc2d3-acd4 b3cd3-a2c2d3 ac3d3-b2cd4 c4d3-bcd5 bcd4-ad5 b3d4|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| bc3 0   0   0   bc2d 0    0    0    bcd2 0    0    0    bd3 0   0   0   c4 0|
| 0   bc3 0   0   0    bc2d 0    0    0    bcd2 0    0    0   bd3 0   0   0  c|
| 0   0   bc3 0   0    0    bc2d 0    0    0    bcd2 0    0   0   bd3 0   0  0|
| 0   0   0   bc3 0    0    0    bc2d 0    0    0    bcd2 0   0   0   bd3 0  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-a2cd4 ac2d4-b2d5 c3d4-bd6 a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  0  0  c3d 0   0   0   c2d2 0    0    0    cd3 0   0   0   d4 0  0  0  |, {2|
|4 0  0  0   c3d 0   0   0    c2d2 0    0    0   cd3 0   0   0  d4 0  0  |  {3|
|  c4 0  0   0   c3d 0   0    0    c2d2 0    0   0   cd3 0   0  0  d4 0  |  {3|
|  0  c4 0   0   0   c3d 0    0    0    c2d2 0   0   0   cd3 0  0  0  d4 |  {3|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b2c ab2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|} | -a4b2 -a5c -a4bd -a4c2 -a3b3 -a4bc -a3b2d -a3bc2 -a3b2c -a4c2 -a3bcd -a3c|
|} | a4c   a4d  0     0     a3bc  a3bd  0      0      a3c2   a3cd  0      0   |
|} | a5    a4b  -a4c  -a4d  a4b   a3b2  -a3bc  -a3bd  a4c    a3bc  -a3c2  -a3c|
|} | 0     0    a5    a4b   0     0     a4b    a3b2   0      0     a4c    a3bc|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bcd2 bd3 c4 c3d c2d2 cd3 d4 |, | a4bc-a5d a4b3-a6c a5c2-a4b2d a4c3-a4bd2 a3b2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|3 -a3b2d -a4cd -a3bd2 -a3c2d -a2b4 -a3b2c -a2b3d -a2b2c2 -a2b3c -a3bc2 -a2b2c|
|  a3cd   a3d2  0      0      a2b2c a2b2d  0      0       a2bc2  a2bcd  0     |
|d a4d    a3bd  -a3cd  -a3d2  a3b2  a2b3   -a2b2c -a2b2d  a3bc   a2b2c  -a2bc2|
|  0      0     a4d    a3bd   0     0      a3b2   a2b3    0      0      a3bc  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c-a4bd a3b4-a5bc a4bc2-a3b3d a3bc3-a3b2d2 a3bc2-a4cd a3b3c-a5c2 a4c3-a3b2cd a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d -a2bc3 -a2b3d -a3bcd -a2b2d2 -a2bc2d -a2b2c2 -a3c3 -a2bc2d -a2c4  -a2b2cd -|
|  0      a2bcd  a2bd2  0       0       a2c3    a2c2d 0       0      a2c2d   a|
|  -a2bcd a3bd   a2b2d  -a2bcd  -a2bd2  a3c2    a2bc2 -a2c3   -a2c2d a3cd    a|
|  a2b2c  0      0      a3bd    a2b2d   0       0     a3c2    a2bc2  0       0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3c4-a3bcd2 a3bcd-a4d2 a3b3d-a5cd a4c2d-a3b2d2 a3c3d-a3bd3 a2b3c-a3b2d a2b5-a4|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|a3c2d -a2bcd2 -a2c3d -a2b2d2 -a3cd2 -a2bd3 -a2c2d2 -ab5 -a2b3c -ab4d -ab3c2 -|
|2cd2  0       0      a2cd2   a2d3   0      0       ab3c ab3d   0     0      a|
|2bcd  -a2c2d  -a2cd2 a3d2    a2bd2  -a2cd2 -a2d3   a2b3 ab4    -ab3c -ab3d  a|
|      a3cd    a2bcd  0       0      a3d2   a2bd2   0    0      a2b3  ab4    0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b2c a3b2c2-a2b4d a2b2c3-a2b3d2 a2b2c2-a3bcd a2b4c-a4bc2 a3bc3-a2b3cd a2bc4-a2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|ab4c -a2b2c2 -ab3cd -ab2c3 -ab4d -a2b2cd -ab3d2 -ab2c2d -ab3c2 -a2bc3 -ab2c2d|
|b2c2 ab2cd   0      0      ab2cd ab2d2   0      0       abc3   abc2d  0      |
|2b2c ab3c    -ab2c2 -ab2cd a2b2d ab3d    -ab2cd -ab2d2  a2bc2  ab2c2  -abc3  |
|     0       a2b2c  ab3c   0     0       a2b2d  ab3d    0      0      a2bc2  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b2cd2 a2b2cd-a3bd2 a2b4d-a4bcd a3bc2d-a2b3d2 a2bc3d-a2b2d3 a2bc3-a3c2d a2b3c2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| -abc4  -ab3cd -a2bc2d -ab2cd2 -abc3d -ab3d2 -a2bcd2 -ab2d3 -abc2d2 -ab2c3 -a|
| 0      abc2d  abcd2   0       0      abcd2  abd3    0      0       ac4    ac|
| -abc2d a2bcd  ab2cd   -abc2d  -abcd2 a2bd2  ab2d2   -abcd2 -abd3   a2c3   ab|
| ab2c2  0      0       a2bcd   ab2cd  0      0       a2bd2  ab2d2   0      0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-a4c3 a3c4-a2b2c2d a2c5-a2bc2d2 a2bc2d-a3cd2 a2b3cd-a4c2d a3c3d-a2b2cd2 a2c4d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2c4 -abc3d -ac5  -ab2c2d -a2c3d -abc2d2 -ac4d  -ab2cd2 -a2c2d2 -abcd3 -ac3d2 |
|3d  0      0     ac3d    ac2d2  0       0      ac2d2   acd3    0      0      |
|c3  -ac4   -ac3d a2c2d   abc2d  -ac3d   -ac2d2 a2cd2   abcd2   -ac2d2 -acd3  |
|    a2c3   abc3  0       0      a2c2d   abc2d  0       0       a2cd2  abcd2  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-a2bcd3 a2bcd2-a3d3 a2b3d2-a4cd2 a3c2d2-a2b2d3 a2c3d2-a2bd4 ab4c-a2b3d ab6-a3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-ab2d3 -a2cd3 -abd4 -ac2d3 -b6 -ab4c -b5d -b4c2 -b5c -ab3c2 -b4cd -b3c3 -b5d |
|acd3   ad4    0     0      b4c b4d   0    0     b3c2 b3cd   0     0     b3cd |
|a2d3   abd3   -acd3 -ad4   ab4 b5    -b4c -b4d  ab3c b4c    -b3c2 -b3cd ab3d |
|0      0      a2d3  abd3   0   0     ab4  b5    0    0      ab3c  b4c   0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b3c a2b3c2-ab5d ab3c3-ab4d2 ab3c2-a2b2cd ab5c-a3b2c2 a2b2c3-ab4cd ab2c4-ab3cd|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-ab3cd -b4d2 -b3c2d -b4c2 -ab2c3 -b3c2d -b2c4  -b4cd -ab2c2d -b3cd2 -b2c3d -b|
|b3d2   0     0      b2c3  b2c2d  0      0      b2c2d b2cd2   0      0      b2|
|b4d    -b3cd -b3d2  ab2c2 b3c2   -b2c3  -b2c2d ab2cd b3cd    -b2c2d -b2cd2 ab|
|0      ab3d  b4d    0     0      ab2c2  b3c2   0     0       ab2cd  b3cd   0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2 ab3cd-a2b2d2 ab5d-a3b2cd a2b2c2d-ab4d2 ab2c3d-ab3d3 ab2c3-a2bc2d ab4c2-a3bc|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|4d2 -ab2cd2 -b3d3  -b2c2d2 -b3c3 -abc4 -b2c3d -bc5  -b3c2d -abc3d -b2c2d2 -bc|
|cd2 b2d3    0      0       bc4   bc3d  0      0     bc3d   bc2d2  0       0  |
|2d2 b3d2    -b2cd2 -b2d3   abc3  b2c3  -bc4   -bc3d abc2d  b2c2d  -bc3d   -bc|
|    0       ab2d2  b3d2    0     0     abc3   b2c3  0      0      abc2d   b2c|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3 a2bc4-ab3c2d abc5-ab2c2d2 ab2c2d-a2bcd2 ab4cd-a3bc2d a2bc3d-ab3cd2 abc4d-ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|4d  -b3cd2 -abc2d2 -b2cd3 -bc3d2 -b3d3 -abcd3 -b2d4 -bc2d3 -b2c4 -ac5 -bc4d -|
|    bc2d2  bcd3    0      0      bcd3  bd4    0     0      c5    c4d  0     0|
|2d2 abcd2  b2cd2   -bc2d2 -bcd3  abd3  b2d3   -bcd3 -bd4   ac4   bc4  -c5   -|
|2d  0      0       abcd2  b2cd2  0     0      abd3  b2d3   0     0    ac4   b|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2cd3 ab2cd2-a2bd3 ab4d2-a3bcd2 a2bc2d2-ab3d3 abc3d2-ab2d4 abc4-a2c3d ab3c3-a3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c6  -b2c3d -ac4d -bc3d2 -c5d  -b2c2d2 -ac3d2 -bc2d3 -c4d2 -b2cd3 -ac2d3 -bcd4|
|    c4d    c3d2  0      0     c3d2    c2d3   0      0     c2d3   cd4    0    |
|c4d ac3d   bc3d  -c4d   -c3d2 ac2d2   bc2d2  -c3d2  -c2d3 acd3   bcd3   -c2d3|
|c4  0      0     ac3d   bc3d  0       0      ac2d2  bc2d2 0      0      acd3 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c4 a2c5-ab2c3d ac6-abc3d2 abc3d-a2c2d2 ab3c2d-a3c3d a2c4d-ab2c2d2 ac5d-abc2d3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| -c3d3 -b2d4 -acd4 -bd5 -c2d4 a4 0  0  0  a3b 0   0   0   a3c 0   0   0   a3d|
| 0     cd4   d5    0    0     0  a4 0  0  0   a3b 0   0   0   a3c 0   0   0  |
| -cd4  ad4   bd4   -cd4 -d5   0  0  a4 0  0   0   a3b 0   0   0   a3c 0   0  |
| bcd3  0     0     ad4  bd4   0  0  0  a4 0   0   0   a3b 0   0   0   a3c 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| abc2d2-a2cd3 ab3cd2-a3c2d2 a2c3d2-ab2cd3 ac4d2-abcd4 abcd3-a2d4 ab3d3-a3cd3 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   0   0   a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    a2c2|
| a3d 0   0   0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0   |
| 0   a3d 0   0    0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0   |
| 0   0   a3d 0    0    0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a2c2d3-ab2d4 ac3d3-abd5 b5c-ab4d b7-a2b4c ab4c2-b6d b4c3-b5d2 b4c2-ab3cd b6c-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0    0    0    a2cd 0    0    0    a2d2 0    0    0    ab3 0   0   0   ab2c |
| a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0    0   ab3 0   0   0    |
| 0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0   0   ab3 0   0    |
| 0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0   0   0   ab3 0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a2b3c2 ab3c3-b5cd b3c4-b4cd2 b4cd-ab3d2 b6d-a2b3cd ab3c2d-b5d2 b3c3d-b4d3 b3c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0    ab|
|ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0 |
|0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0 |
|0    0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3-ab2c2d b5c2-a2b2c3 ab2c4-b4c2d b2c5-b3c2d2 b3c2d-ab2cd2 b5cd-a2b2c2d ab2c3d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d2 0    0    0    ac3 0   0   0   ac2d 0    0    0    acd2 0    0    0    ad3|
|   abd2 0    0    0   ac3 0   0   0    ac2d 0    0    0    acd2 0    0    0  |
|   0    abd2 0    0   0   ac3 0   0    0    ac2d 0    0    0    acd2 0    0  |
|   0    0    abd2 0   0   0   ac3 0    0    0    ac2d 0    0    0    acd2 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-b4cd2 b2c4d-b3cd3 b3cd2-ab2d3 b5d2-a2b2cd2 ab2c2d2-b4d3 b2c3d2-b3d4 b2c4-abc|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   0   0   b4 0  0  0  b3c 0   0   0   b3d 0   0   0   b2c2 0    0    0    |
| ad3 0   0   0  b4 0  0  0   b3c 0   0   0   b3d 0   0   0    b2c2 0    0    |
| 0   ad3 0   0  0  b4 0  0   0   b3c 0   0   0   b3d 0   0    0    b2c2 0    |
| 0   0   ad3 0  0  0  b4 0   0   0   b3c 0   0   0   b3d 0    0    0    b2c2 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3d b4c3-a2bc4 abc5-b3c3d bc6-b2c3d2 b2c3d-abc2d2 b4c2d-a2bc3d abc4d-b3c2d2 bc|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|b2cd 0    0    0    b2d2 0    0    0    bc3 0   0   0   bc2d 0    0    0    b|
|0    b2cd 0    0    0    b2d2 0    0    0   bc3 0   0   0    bc2d 0    0    0|
|0    0    b2cd 0    0    0    b2d2 0    0   0   bc3 0   0    0    bc2d 0    0|
|0    0    0    b2cd 0    0    0    b2d2 0   0   0   bc3 0    0    0    bc2d 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|5d-b2c2d3 b2c2d2-abcd3 b4cd2-a2bc2d2 abc3d2-b3cd3 bc4d2-b2cd4 b2cd3-abd4 b4d3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|cd2 0    0    0    bd3 0   0   0   c4 0  0  0  c3d 0   0   0   c2d2 0    0   |
|    bcd2 0    0    0   bd3 0   0   0  c4 0  0  0   c3d 0   0   0    c2d2 0   |
|    0    bcd2 0    0   0   bd3 0   0  0  c4 0  0   0   c3d 0   0    0    c2d2|
|    0    0    bcd2 0   0   0   bd3 0  0  0  c4 0   0   0   c3d 0    0    0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-a2bcd3 abc2d3-b3d4 bc3d3-b2d5 bc5-ac4d b3c4-a2c5 ac6-b2c4d c7-bc4d2 bc4d-ac3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0    cd3 0   0   0   d4 0  0  0  |)                                         |
| 0    0   cd3 0   0   0  d4 0  0  |                                          |
| 0    0   0   cd3 0   0  0  d4 0  |                                          |
| c2d2 0   0   0   cd3 0  0  0  d4 |                                          |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2 b3c3d-a2c4d ac5d-b2c3d2 c6d-bc3d3 bc3d2-ac2d3 b3c2d2-a2c3d2 ac4d2-b2c2d3 c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|5d2-bc2d4 bc2d3-acd4 b3cd3-a2c2d3 ac3d3-b2cd4 c4d3-bcd5 bcd4-ad5 b3d4-a2cd4 a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2d4-b2d5 c3d4-bd6 a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab2d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 bd3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|----------------------+------------------------------------------------------|
|                      |subquotient ({4} | a2 0  0  0  ab 0  0  0  ac 0  0  0 |
|                      |             {4} | 0  a2 0  0  0  ab 0  0  0  ac 0  0 |
|                      |             {4} | 0  0  a2 0  0  0  ab 0  0  0  ac 0 |
|                      |             {4} | 0  0  0  a2 0  0  0  ab 0  0  0  ac|
|                      |                                                      |
|                      |{-2, 4}                                               |
|----------------------+------------------------------------------------------|
| c4 c3d c2d2 cd3 d4 |)|subquotient ({2} | a2 0  0  0  ab 0  0  0  ac 0  0  0 |
|                      |             {3} | 0  a2 0  0  0  ab 0  0  0  ac 0  0 |
|                      |             {3} | 0  0  a2 0  0  0  ab 0  0  0  ac 0 |
|                      |             {3} | 0  0  0  a2 0  0  0  ab 0  0  0  ac|
|                      |                                                      |
|                      |{-2, 3}                                               |
|----------------------+------------------------------------------------------|
|                      |subquotient (| a2 ab ac ad b2 bc bd c2 cd d2 a3bc-a4d |
|                      |                                                      |
|                      |{-2, 2}                                               |
|                      |                                                      |
|                      |                                                      |
|                      |                                                      |
|----------------------+------------------------------------------------------|
|                      |0                                                     |
|                      |                                                      |
|                      |{-2, 1}                                               |
|                      |                                                      |
|                      |                                                      |
|                      |                                                      |
|----------------------+------------------------------------------------------|
|                      |0                                                     |
|                      |                                                      |
|                      |{-2, 0}                                               |
|----------------------+------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0|
| 0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d|
| 0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0|
| 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0|
| 0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d|
| 0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0|
| 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a3b3-a5c a4c2-a3b2d a3c3-a3bd2 a2b2c-a3bd a2b4-a4bc a3bc2-a2b3d a2bc3-a2b2d2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  0  0  a3d  a2bd  a2cd  a2d2  ab2d  abcd  abd2  ac2d  acd2  ad3   b3d  b2cd |
|2 0  0  -a3c -a2bc -a2c2 -a2cd -ab2c -abc2 -abcd -ac3  -ac2d -acd2 -b3c -b2c2|
|  d2 0  -a3b -a2b2 -a2bc -a2bd -ab3  -ab2c -ab2d -abc2 -abcd -abd2 -b4  -b3c |
|  0  d2 a4   a3b   a3c   a3d   a2b2  a2bc  a2bd  a2c2  a2cd  a2d2  ab3  ab2c |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  0  0  -a3b2 -a4c -a3bd -a3c2 -a2b3 -a3bc -a2b2d -a2bc2 -a2b2c -a3c2 -a2bcd |
|2 0  0  a3c   a3d  0     0     a2bc  a2bd  0      0      a2c2   a2cd  0      |
|  d2 0  a4    a3b  -a3c  -a3d  a3b   a2b2  -a2bc  -a2bd  a3c    a2bc  -a2c2  |
|  0  d2 0     0    a4    a3b   0     0     a3b    a2b2   0      0     a3c    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a2bc2-a3cd a2b3c-a4c2 a3c3-a2b2cd a2c4-a2bcd2 a2bcd-a3d2 a2b3d-a4cd a3c2d-a2b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| b2d2  bc2d  bcd2  bd3   c3d  c2d2  cd3   d4   a3 0  0  0  a2b 0   0   0   a2|
| -b2cd -bc3  -bc2d -bcd2 -c4  -c3d  -c2d2 -cd3 0  a3 0  0  0   a2b 0   0   0 |
| -b3d  -b2c2 -b2cd -b2d2 -bc3 -bc2d -bcd2 -bd3 0  0  a3 0  0   0   a2b 0   0 |
| ab2d  abc2  abcd  abd2  ac3  ac2d  acd2  ad3  0  0  0  a3 0   0   0   a2b 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-a2c3 -a2b2d -a3cd -a2bd2 -a2c2d -ab4 -a2b2c -ab3d -ab2c2 -ab3c -a2bc2 -ab2cd|
|0     a2cd   a2d2  0      0      ab2c ab2d   0     0      abc2  abcd   0     |
|-a2cd a3d    a2bd  -a2cd  -a2d2  a2b2 ab3    -ab2c -ab2d  a2bc  ab2c   -abc2 |
|a2bc  0      0     a3d    a2bd   0    0      a2b2  ab3    0     0      a2bc  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2d2 a2c3d-a2bd3 ab3c-a2b2d ab5-a3b2c a2b2c2-ab4d ab2c3-ab3d2 ab2c2-a2bcd ab4c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0  |
|  a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0  |
|  0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0  |
|  0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| -abc3 -ab3d -a2bcd -ab2d2 -abc2d -ab2c2 -a2c3 -abc2d -ac4  -ab2cd -a2c2d -ab|
| 0     abcd  abd2   0      0      ac3    ac2d  0      0     ac2d   acd2   0  |
| -abcd a2bd  ab2d   -abcd  -abd2  a2c2   abc2  -ac3   -ac2d a2cd   abcd   -ac|
| ab2c  0     0      a2bd   ab2d   0      0     a2c2   abc2  0      0      a2c|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-a3bc2 a2bc3-ab3cd abc4-ab2cd2 ab2cd-a2bd2 ab4d-a3bcd a2bc2d-ab3d2 abc3d-ab2d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| ac2 0   0   0   acd 0   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   |
| 0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   |
| 0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   |
| 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|cd2 -ac3d -ab2d2 -a2cd2 -abd3 -ac2d2 -b5 -ab3c -b4d -b3c2 -b4c -ab2c2 -b3cd -|
|    0     acd2   ad3    0     0      b3c b3d   0    0     b2c2 b2cd   0     0|
|2d  -acd2 a2d2   abd2   -acd2 -ad3   ab3 b4    -b3c -b3d  ab2c b3c    -b2c2 -|
|d   abcd  0      0      a2d2  abd2   0   0     ab3  b4    0    0      ab2c  b|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3 abc3-a2c2d ab3c2-a3c3 a2c4-ab2c2d ac5-abc2d2 abc2d-a2cd2 ab3cd-a3c2d a2c3d-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c|
|0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0|
|0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0|
|0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b2c3 -b4d -ab2cd -b3d2 -b2c2d -b3c2 -abc3 -b2c2d -bc4  -b3cd -abc2d -b2cd2 -b|
|     b2cd b2d2   0     0      bc3   bc2d  0      0     bc2d  bcd2   0      0 |
|b2cd ab2d b3d    -b2cd -b2d2  abc2  b2c2  -bc3   -bc2d abcd  b2cd   -bc2d  -b|
|3c   0    0      ab2d  b3d    0     0     abc2   b2c2  0     0      abcd   b2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|ab2cd2 ac4d-abcd3 abcd2-a2d3 ab3d2-a3cd2 a2c2d2-ab2d3 ac3d2-abd4 b4c-ab3d b6-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2d 0   0   0   cd2 0   0   0   d3 0  0  0  |, {4} | a3d  a2bd  a2cd  a2d2  ab|
|   c2d 0   0   0   cd2 0   0   0  d3 0  0  |  {4} | -a3c -a2bc -a2c2 -a2cd -a|
|   0   c2d 0   0   0   cd2 0   0  0  d3 0  |  {4} | -a3b -a2b2 -a2bc -a2bd -a|
|   0   0   c2d 0   0   0   cd2 0  0  0  d3 |  {4} | a4   a3b   a3c   a3d   a2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c3d -b3d2 -abcd2 -b2d3 -bc2d2 -b2c3 -ac4 -bc3d -c5  -b2c2d -ac3d -bc2d2 -c4d |
|    bcd2  bd3    0     0      c4    c3d  0     0    c3d    c2d2  0      0    |
|cd2 abd2  b2d2   -bcd2 -bd3   ac3   bc3  -c4   -c3d ac2d   bc2d  -c3d   -c2d2|
|cd  0     0      abd2  b2d2   0     0    ac3   bc3  0      0     ac2d   bc2d |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a2b3c ab3c2-b5d b3c3-b4d2 b3c2-ab2cd b5c-a2b2c2 ab2c3-b4cd b2c4-b3cd2 b3cd-ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2d  abcd  abd2  ac2d  acd2  ad3   b3d  b2cd  b2d2  bc2d  bcd2  bd3   c3d  c2d|
|b2c -abc2 -abcd -ac3  -ac2d -acd2 -b3c -b2c2 -b2cd -bc3  -bc2d -bcd2 -c4  -c3|
|b3  -ab2c -ab2d -abc2 -abcd -abd2 -b4  -b3c  -b3d  -b2c2 -b2cd -b2d2 -bc3 -bc|
|b2  a2bc  a2bd  a2c2  a2cd  a2d2  ab3  ab2c  ab2d  abc2  abcd  abd2  ac3  ac2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| -b2cd2 -ac2d2 -bcd3 -c3d2 -b2d3 -acd3 -bd4 -c2d3 a3 0  0  0  a2b 0   0   0  |
| c2d2   cd3    0     0     cd3   d4    0    0     0  a3 0  0  0   a2b 0   0  |
| acd2   bcd2   -c2d2 -cd3  ad3   bd3   -cd3 -d4   0  0  a3 0  0   0   a2b 0  |
| 0      0      acd2  bcd2  0     0     ad3  bd3   0  0  0  a3 0   0   0   a2b|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2d2 b5d-a2b2cd ab2c2d-b4d2 b2c3d-b3d3 b2c3-abc2d b4c2-a2bc3 abc4-b3c2d bc5-b2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2  cd3   d4   a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2|
|d  -c2d2 -cd3 0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0  |
|2d -bcd2 -bd3 0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0  |
|d  acd2  ad3  0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   a2d 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   |
| 0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   |
| 0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd |
| 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2d2 b2c2d-abcd2 b4cd-a2bc2d abc3d-b3cd2 bc4d-b2cd3 b2cd2-abd3 b4d2-a2bcd2 ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   |
| ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   |
| 0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   |
| 0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0|
|0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0|
|0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0|
|abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2d2-b3d3 bc3d2-b2d4 bc4-ac3d b3c3-a2c4 ac5-b2c3d c6-bc3d2 bc3d-ac2d2 b3c2d-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   b|
|0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0|
|0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0|
|0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0   bc2 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0|
|   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0|
|   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0|
|2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2c3d ac4d-b2c2d2 c5d-bc2d3 bc2d2-acd3 b3cd2-a2c2d2 ac3d2-b2cd3 c4d2-bcd4 bcd3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|cd 0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0   0   d3|
|   bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0   0   0 |
|   0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2 0   0 |
|   0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0   cd2 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  c2d 0   0   0   cd2 0   0   0   d3 0  0  0  |, {2} | -a3b2 -a4c -a3bd -a3c2|
|  0   c2d 0   0   0   cd2 0   0   0  d3 0  0  |  {3} | a3c   a3d  0     0    |
|  0   0   c2d 0   0   0   cd2 0   0  0  d3 0  |  {3} | a4    a3b  -a3c  -a3d |
|3 0   0   0   c2d 0   0   0   cd2 0  0  0  d3 |  {3} | 0     0    a4    a3b  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-ad4 b3d3-a2cd3 ac2d3-b2d4 c3d3-bd5 a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0  0  0  |)                                                                 |
| d3 0  0  |                                                                  |
| 0  d3 0  |                                                                  |
| 0  0  d3 |                                                                  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| -a2b3 -a3bc -a2b2d -a2bc2 -a2b2c -a3c2 -a2bcd -a2c3 -a2b2d -a3cd -a2bd2 -a2c|
| a2bc  a2bd  0      0      a2c2   a2cd  0      0     a2cd   a2d2  0      0   |
| a3b   a2b2  -a2bc  -a2bd  a3c    a2bc  -a2c2  -a2cd a3d    a2bd  -a2cd  -a2d|
| 0     0     a3b    a2b2   0      0     a3c    a2bc  0      0     a3d    a2bd|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| b2c b2d bc2 bcd bd2 c3 c2d cd2 d3 |, | a3bc-a4d a3b3-a5c a4c2-a3b2d a3c3-a3b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2d -ab4 -a2b2c -ab3d -ab2c2 -ab3c -a2bc2 -ab2cd -abc3 -ab3d -a2bcd -ab2d2 -ab|
|   ab2c ab2d   0     0      abc2  abcd   0      0     abcd  abd2   0      0  |
|2  a2b2 ab3    -ab2c -ab2d  a2bc  ab2c   -abc2  -abcd a2bd  ab2d   -abcd  -ab|
|   0    0      a2b2  ab3    0     0      a2bc   ab2c  0     0      a2bd   ab2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2 a2b2c-a3bd a2b4-a4bc a3bc2-a2b3d a2bc3-a2b2d2 a2bc2-a3cd a2b3c-a4c2 a3c3-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2d -ab2c2 -a2c3 -abc2d -ac4  -ab2cd -a2c2d -abcd2 -ac3d -ab2d2 -a2cd2 -abd3 |
|    ac3    ac2d  0      0     ac2d   acd2   0      0     acd2   ad3    0     |
|d2  a2c2   abc2  -ac3   -ac2d a2cd   abcd   -ac2d  -acd2 a2d2   abd2   -acd2 |
|d   0      0     a2c2   abc2  0      0      a2cd   abcd  0      0      a2d2  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2b2cd a2c4-a2bcd2 a2bcd-a3d2 a2b3d-a4cd a3c2d-a2b2d2 a2c3d-a2bd3 ab3c-a2b2d a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-ac2d2 -b5 -ab3c -b4d -b3c2 -b4c -ab2c2 -b3cd -b2c3 -b4d -ab2cd -b3d2 -b2c2d |
|0      b3c b3d   0    0     b2c2 b2cd   0     0     b2cd b2d2   0     0      |
|-ad3   ab3 b4    -b3c -b3d  ab2c b3c    -b2c2 -b2cd ab2d b3d    -b2cd -b2d2  |
|abd2   0   0     ab3  b4    0    0      ab2c  b3c   0    0      ab2d  b3d    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b5-a3b2c a2b2c2-ab4d ab2c3-ab3d2 ab2c2-a2bcd ab4c-a3bc2 a2bc3-ab3cd abc4-ab2c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-b3c2 -abc3 -b2c2d -bc4  -b3cd -abc2d -b2cd2 -bc3d -b3d2 -abcd2 -b2d3 -bc2d2 |
|bc3   bc2d  0      0     bc2d  bcd2   0      0     bcd2  bd3    0     0      |
|abc2  b2c2  -bc3   -bc2d abcd  b2cd   -bc2d  -bcd2 abd2  b2d2   -bcd2 -bd3   |
|0     0     abc2   b2c2  0     0      abcd   b2cd  0     0      abd2  b2d2   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2 ab2cd-a2bd2 ab4d-a3bcd a2bc2d-ab3d2 abc3d-ab2d3 abc3-a2c2d ab3c2-a3c3 a2c4|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-b2c3 -ac4 -bc3d -c5  -b2c2d -ac3d -bc2d2 -c4d  -b2cd2 -ac2d2 -bcd3 -c3d2 -b2|
|c4    c3d  0     0    c3d    c2d2  0      0     c2d2   cd3    0     0     cd3|
|ac3   bc3  -c4   -c3d ac2d   bc2d  -c3d   -c2d2 acd2   bcd2   -c2d2 -cd3  ad3|
|0     0    ac3   bc3  0      0     ac2d   bc2d  0      0      acd2  bcd2  0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-ab2c2d ac5-abc2d2 abc2d-a2cd2 ab3cd-a3c2d a2c3d-ab2cd2 ac4d-abcd3 abcd2-a2d3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d3 -acd3 -bd4 -c2d3 a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   0|
|   d4    0    0     0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   0|
|   bd3   -cd3 -d4   0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d 0|
|   0     ad3  bd3   0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   a|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| ab3d2-a3cd2 a2c2d2-ab2d3 ac3d2-abd4 b4c-ab3d b6-a2b3c ab3c2-b5d b3c3-b4d2 b3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0 |
|   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0 |
|   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   ac|
|2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2-ab2cd b5c-a2b2c2 ab2c3-b4cd b2c4-b3cd2 b3cd-ab2d2 b5d-a2b2cd ab2c2d-b4d2 b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0  |
|  0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0  |
|d 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc2|
|  acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2c3d-b3d3 b2c3-abc2d b4c2-a2bc3 abc4-b3c2d bc5-b2c2d2 b2c2d-abcd2 b4cd-a2bc2d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0   |
| 0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0   |
| 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2 |
| bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| abc3d-b3cd2 bc4d-b2cd3 b2cd2-abd3 b4d2-a2bcd2 abc2d2-b3d3 bc3d2-b2d4 bc4-ac3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|0   d3 0  0  0  |)                                                           |
|0   0  d3 0  0  |                                                            |
|0   0  0  d3 0  |                                                            |
|cd2 0  0  0  d3 |                                                            |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d b3c3-a2c4 ac5-b2c3d c6-bc3d2 bc3d-ac2d2 b3c2d-a2c3d ac4d-b2c2d2 c5d-bc2d3 b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2d2-acd3 b3cd2-a2c2d2 ac3d2-b2cd3 c4d2-bcd4 bcd3-ad4 b3d3-a2cd3 ac2d3-b2d4 c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3d3-bd5 a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3 b2c b2d bc2 bcd bd2 c3 c2d |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|---------+-------------------------------------------------------------------|
|         |subquotient ({5} | a b c d a2 ab ac ad b2 bc bd c2 cd d2 |, {5} | a|
|         |                                                                   |
|         |{-1, 4}                                                            |
|         |                                                                   |
|         |                                                                   |
|         |                                                                   |
|---------+-------------------------------------------------------------------|
|         |subquotient ({4} | a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 a2d  abd  acd  a|
|         |             {4} | 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 -a2c -abc -ac2 -|
|         |             {4} | 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 -a2b -ab2 -abc -|
|         |             {4} | 0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d a3   a2b  a2c  a|
|         |                                                                   |
|         |{-1, 3}                                                            |
|---------+-------------------------------------------------------------------|
|cd2 d3 |)|subquotient ({2} | a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 -a2b2 -a3c -a2bd|
|         |             {3} | 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 a2c   a2d  0    |
|         |             {3} | 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 a3    a2b  -a2c |
|         |             {3} | 0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0     0    a3   |
|         |                                                                   |
|         |{-1, 2}                                                            |
|---------+-------------------------------------------------------------------|
|         |subquotient (| a b c d a2bc-a3d a2b3-a4c a3c2-a2b2d a2c3-a2bd2 ab2c|
|         |                                                                   |
|         |{-1, 1}                                                            |
|         |                                                                   |
|         |                                                                   |
|         |                                                                   |
|---------+-------------------------------------------------------------------|
|         |0                                                                  |
|         |                                                                   |
|         |{-1, 0}                                                            |
|---------+-------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2 ab ac ad b2 bc bd c2 cd d2 |)                                              |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2  b2d  bcd  bd2  c2d  cd2  d3   a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0|
|acd -b2c -bc2 -bcd -c3  -c2d -cd2 0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0|
|abd -b3  -b2c -b2d -bc2 -bcd -bd2 0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  a|
|2d  ab2  abc  abd  ac2  acd  ad2  0  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| -a2c2 -ab3 -a2bc -ab2d -abc2 -ab2c -a2c2 -abcd -ac3 -ab2d -a2cd -abd2 -ac2d |
| 0     abc  abd   0     0     ac2   acd   0     0    acd   ad2   0     0     |
| -a2d  a2b  ab2   -abc  -abd  a2c   abc   -ac2  -acd a2d   abd   -acd  -ad2  |
| a2b   0    0     a2b   ab2   0     0     a2c   abc  0     0     a2d   abd   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-a2bd ab4-a3bc a2bc2-ab3d abc3-ab2d2 abc2-a2cd ab3c-a3c2 a2c3-ab2cd ac4-abcd2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |
|  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |
|d 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |
|  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-b4 -ab2c -b3d -b2c2 -b3c -abc2 -b2cd -bc3 -b3d -abcd -b2d2 -bc2d -b2c2 -ac3 |
|b2c b2d   0    0     bc2  bcd   0     0    bcd  bd2   0     0     c3    c2d  |
|ab2 b3    -b2c -b2d  abc  b2c   -bc2  -bcd abd  b2d   -bcd  -bd2  ac2   bc2  |
|0   0     ab2  b3    0    0     abc   b2c  0    0     abd   b2d   0     0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| abcd-a2d2 ab3d-a3cd a2c2d-ab2d2 ac3d-abd3 b3c-ab2d b5-a2b2c ab2c2-b4d b2c3-b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
||, {4} | a2d  abd  acd  ad2  b2d  bcd  bd2  c2d  cd2  d3   a2 0  0  0  ab 0  |
||  {4} | -a2c -abc -ac2 -acd -b2c -bc2 -bcd -c3  -c2d -cd2 0  a2 0  0  0  ab |
||  {4} | -a2b -ab2 -abc -abd -b3  -b2c -b2d -bc2 -bcd -bd2 0  0  a2 0  0  0  |
||  {4} | a3   a2b  a2c  a2d  ab2  abc  abd  ac2  acd  ad2  0  0  0  a2 0  0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-bc2d -c4  -b2cd -ac2d -bcd2 -c3d -b2d2 -acd2 -bd3 -c2d2 a2 0  0  0  ab 0  0 |
|0     0    c2d   cd2   0     0    cd2   d3    0    0     0  a2 0  0  0  ab 0 |
|-c3   -c2d acd   bcd   -c2d  -cd2 ad2   bd2   -cd2 -d3   0  0  a2 0  0  0  ab|
|ac2   bc2  0     0     acd   bcd  0     0     ad2  bd2   0  0  0  a2 0  0  0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3d2 b2c2-abcd b4c-a2bc2 abc3-b3cd bc4-b2cd2 b2cd-abd2 b4d-a2bcd abc2d-b3d2 bc|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0 |
|0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0 |
|ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0 |
|0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  c|
| 0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0|
| 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0|
| ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3d-b2d3 bc3-ac2d b3c2-a2c3 ac4-b2c2d c5-bc2d2 bc2d-acd2 b3cd-a2c2d ac3d-b2cd2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| cd 0  0  0  d2 0  0  0  |)                                                  |
| 0  cd 0  0  0  d2 0  0  |                                                   |
| 0  0  cd 0  0  0  d2 0  |                                                   |
| 0  0  0  cd 0  0  0  d2 |                                                   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d 0  0  0  d2 0  0  0  |, {2} | -a2b2 -a3c -a2bd -a2c2 -ab3 -a2bc -ab2d -abc2|
|  cd 0  0  0  d2 0  0  |  {3} | a2c   a2d  0     0     abc  abd   0     0    |
|  0  cd 0  0  0  d2 0  |  {3} | a3    a2b  -a2c  -a2d  a2b  ab2   -abc  -abd |
|  0  0  cd 0  0  0  d2 |  {3} | 0     0    a3    a2b   0    0     a2b   ab2  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| c4d-bcd3 bcd2-ad3 b3d2-a2cd2 ac2d2-b2d3 c3d2-bd4 a2 ab ac ad b2 bc bd c2 cd |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| -ab2c -a2c2 -abcd -ac3 -ab2d -a2cd -abd2 -ac2d -b4 -ab2c -b3d -b2c2 -b3c -ab|
| ac2   acd   0     0    acd   ad2   0     0     b2c b2d   0    0     bc2  bcd|
| a2c   abc   -ac2  -acd a2d   abd   -acd  -ad2  ab2 b3    -b2c -b2d  abc  b2c|
| 0     0     a2c   abc  0     0     a2d   abd   0   0     ab2  b3    0    0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2 |, | a2bc-a3d a2b3-a4c a3c2-a2b2d a2c3-a2bd2 ab2c-a2bd ab4-a3bc a2bc2-ab3d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2 -b2cd -bc3 -b3d -abcd -b2d2 -bc2d -b2c2 -ac3 -bc2d -c4  -b2cd -ac2d -bcd2 |
|   0     0    bcd  bd2   0     0     c3    c2d  0     0    c2d   cd2   0     |
|   -bc2  -bcd abd  b2d   -bcd  -bd2  ac2   bc2  -c3   -c2d acd   bcd   -c2d  |
|   abc   b2c  0    0     abd   b2d   0     0    ac2   bc2  0     0     acd   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| abc3-ab2d2 abc2-a2cd ab3c-a3c2 a2c3-ab2cd ac4-abcd2 abcd-a2d2 ab3d-a3cd a2c2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-c3d -b2d2 -acd2 -bd3 -c2d2 a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b|
|0    cd2   d3    0    0     0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0|
|-cd2 ad2   bd2   -cd2 -d3   0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0|
|bcd  0     0     ad2  bd2   0  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d-ab2d2 ac3d-abd3 b3c-ab2d b5-a2b2c ab2c2-b4d b2c3-b3d2 b2c2-abcd b4c-a2bc2 a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |)    |
|  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |     |
|  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |     |
|  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |     |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bc3-b3cd bc4-b2cd2 b2cd-abd2 b4d-a2bcd abc2d-b3d2 bc3d-b2d3 bc3-ac2d b3c2-a2c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3 ac4-b2c2d c5-bc2d2 bc2d-acd2 b3cd-a2c2d ac3d-b2cd2 c4d-bcd3 bcd2-ad3 b3d2-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|---------------------------------------------------------+-------------------|
|                                                         |0                  |
|                                                         |                   |
|                                                         |{0, 4}             |
|                                                         |                   |
|                                                         |                   |
|                                                         |                   |
|---------------------------------------------------------+-------------------|
|                                                         |cokernel {5} | a b |
|                                                         |                   |
|                                                         |{0, 3}             |
|                                                         |                   |
|                                                         |                   |
|                                                         |                   |
|---------------------------------------------------------+-------------------|
|                                                         |cokernel {4} | ad  |
|                                                         |         {4} | -ac |
|                                                         |         {4} | -ab |
|                                                         |         {4} | a2  |
|                                                         |                   |
|                                                         |{0, 2}             |
|---------------------------------------------------------+-------------------|
|2cd2 ac2d2-b2d3 c3d2-bd4 a2 ab ac ad b2 bc bd c2 cd d2 |)|cokernel {2} | -ab2|
|                                                         |         {3} | ac  |
|                                                         |         {3} | a2  |
|                                                         |         {3} | 0   |
|                                                         |                   |
|                                                         |{0, 1}             |
|---------------------------------------------------------+-------------------|
|                                                         |cokernel | abc-a2d |
|                                                         |                   |
|                                                         |{0, 0}             |
|---------------------------------------------------------+-------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c d |                                                                        |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bd  cd  d2  a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 |                                |
|-bc -c2 -cd 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 |                                |
|-b2 -bc -bd 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 |                                |
|ab  ac  ad  0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d |                                |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| -a2c -abd -ac2 -b3 -abc -b2d -bc2 -b2c -ac2 -bcd -c3 -b2d -acd -bd2 -c2d a 0|
| ad   0    0    bc  bd   0    0    c2   cd   0    0   cd   d2   0    0    0 a|
| ab   -ac  -ad  ab  b2   -bc  -bd  ac   bc   -c2  -cd ad   bd   -cd  -d2  0 0|
| 0    a2   ab   0   0    ab   b2   0    0    ac   bc  0    0    ad   bd   0 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|ab3-a3c a2c2-ab2d ac3-abd2 b2c-abd b4-a2bc abc2-b3d bc3-b2d2 bc2-acd b3c-a2c2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|--------------------------------------------------------------+              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|--------------------------------------------------------------+              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|--------------------------------------------------------------+              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|--------------------------------------------------------------+              |
| 0 0 b 0 0 0 c 0 0 0 d 0 0 0 |                                |              |
| 0 0 0 b 0 0 0 c 0 0 0 d 0 0 |                                |              |
| a 0 0 0 b 0 0 0 c 0 0 0 d 0 |                                |              |
| 0 a 0 0 0 b 0 0 0 c 0 0 0 d |                                |              |
|                                                              |              |
|                                                              |              |
|--------------------------------------------------------------+              |
| ac3-b2cd c4-bcd2 bcd-ad2 b3d-a2cd ac2d-b2d2 c3d-bd3 a b c d ||              |
|                                                              |              |
|                                                              |              |
|--------------------------------------------------------------+              |
+-----------------------------------------------------------------------------+
|i7 : E^0 .dd;                                                                |
+-----------------------------------------------------------------------------+
|i8 : E^infinity                                                              |
|                                                                             |
|     +-----------------------------------------------------------------------|
|o8 = |subquotient (| a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab|
|     |                                                                       |
|     |{-4, 4}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 3}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 2}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 1}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 0}                                                                |
|     +-----------------------------------------------------------------------|
|                                                                             |
|o8 : Page                                                                    |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d3 c4 c3d c2d2 cd3 d4 bc-ad b3-a2c ac2-b2d c3-bd2 0 |, | bc-ad b3-a2c ac2-b2d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|------------+----------------------------------------------------------------|
| c3-bd2 0 |)|subquotient ({2} | 0 a2b2 a2bd a2bd 0 a3c  a3c  a2c2 a2b2 ab3  a|
|            |             {3} | 0 -a2c 0    0    0 -a2d -a2d 0    -a2c -abc 0|
|            |             {3} | 0 -a3  a2c  a2c  0 -a2b -a2b a2d  -a3  -a2b a|
|            |             {3} | 0 0    -a3  -a3  0 0    0    -a2b 0    0    -|
|            |                                                                |
|            |{-3, 4}                                                         |
|------------+----------------------------------------------------------------|
|            |subquotient (| a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3 b2c b2d|
|            |                                                                |
|            |{-3, 3}                                                         |
|            |                                                                |
|            |                                                                |
|            |                                                                |
|------------+----------------------------------------------------------------|
|            |0                                                               |
|            |                                                                |
|            |{-3, 2}                                                         |
|            |                                                                |
|            |                                                                |
|            |                                                                |
|------------+----------------------------------------------------------------|
|            |0                                                               |
|            |                                                                |
|            |{-3, 1}                                                         |
|            |                                                                |
|            |                                                                |
|            |                                                                |
|------------+----------------------------------------------------------------|
|            |0                                                               |
|            |                                                                |
|            |{-3, 0}                                                         |
|------------+----------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|b2d ab2d a2bd a2bc a2bc a2bc abc2 abc2 a2c2 ab2c ab2c abcd abcd abcd 0       |
|    0    0    -abd -abd -abd 0    0    0    -ac2 -ac2 0    0    0    acd     |
|bc  abc  a2c  -ab2 -ab2 -ab2 abd  abd  a2d  -a2c -a2c ac2  ac2  ac2  abc+a2d |
|a2b -a2b -a3  0    0    0    -ab2 -ab2 -a2b 0    0    -a2c -a2c -a2c -a2b    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| bc2 bcd bd2 c3 c2d cd2 d3 bc-ad b3-a2c ac2-b2d c3-bd2 a4 a3b a3c a3d a2b2 a2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|abd2 ac3  abd2 0 a2cd a2cd a2cd ac2d ac2d ab3  ab2c b4   b3d  b3d  ab2d 0    |
|0    0    0    0 -ad2 -ad2 -ad2 0    0    -abc -ac2 -b2c 0    0    0    -ac2+|
|acd  acd  acd  0 -abd -abd -abd ad2  ad2  -a2b -a2c -ab2 b2c  b2c  abc  b3-a2|
|-a2d -abc -a2d 0 0    0    0    -abd -abd 0    0    0    -ab2 -ab2 -a2b 0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|    b2c2 b2c2 abc2 b3c  b3c  b2cd b2cd b2cd abcd 0       b2d2 bc3  b2d2 abd2 |
|b2d 0    0    0    -bc2 -bc2 0    0    0    0    bcd     0    0    0    0    |
|c   b2d  b2d  abd  -abc -abc bc2  bc2  bc2  ac2  b2c+abd bcd  bcd  bcd  acd  |
|    -b3  -b3  -ab2 0    0    -abc -abc -abc -a2c -ab2    -abd -b2c -abd -a2d |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 bd3 c4 c3d c2d2 cd3 d4 |, | bc-ad b3-a2c ac2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0       bc2d bc2d bc3  ac3  0       0        bc2d ac2d 0       bcd2 bcd2 c4  |
|bd2     0    0    0    0    c3      0        0    0    c2d     0    0    0   |
|ac2+b2d bd2  bd2  bcd  acd  ac2+b2d c3-bd2   bd2  ad2  bc2+acd c2d  c2d  c2d |
|-a2c    -b2d -b2d -b2c -abc -b3     -ac2+b2d -b2d -abd -abc    -acd -acd -bc2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-b2d c3-bd2 a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab2d abc2 a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| bcd2 0       bd3  c3d  c3d  0 bd3  0 acd2 acd2 acd2 c2d2 c2d2 0 0 0         |
| 0    cd2     0    0    0    0 0    0 -d3  -d3  -d3  0    0    0 0 -a2cd     |
| c2d  bcd+ad2 cd2  cd2  cd2  0 cd2  0 -bd2 -bd2 -bd2 d3   d3   0 0 -a2bc-a3d |
| -acd -abd    -ad2 -bcd -bcd 0 -ad2 0 0    0    0    -bd2 -bd2 0 0 a3b       |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 bd3 c4 c3d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0         0 0 0 0 0 0 0 0 0 0 0 0 0 0          0 0          0          0 0 0 |
|-a2cd     0 0 0 0 0 0 0 0 0 0 0 0 0 -a2c2+ab2d 0 -abcd      -abcd      0 0 0 |
|-a2bc-a3d 0 0 0 0 0 0 0 0 0 0 0 0 0 ab3-a3c    0 -ab2c-a2bd -ab2c-a2bd 0 0 0 |
|a3b       0 0 0 0 0 0 0 0 0 0 0 0 0 0          0 a2b2       a2b2       0 0 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| c2d2 cd3 d4 |)                                                              |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0 0 0 0         0 0 0 0 0 0 0 0 0 0         0          0         0           |
|0 0 0 -ac3+abd2 0 0 0 0 0 0 0 0 0 -abc2+b3d -a2c2+ab2d -ac3+abd2 -ac3+b2cd+ab|
|0 0 0 0         0 0 0 0 0 0 0 0 0 b4-a2bc   ab3-a3c    0         b3c+ab2d    |
|0 0 0 ab3-a3c   0 0 0 0 0 0 0 0 0 0         0          ab3-a3c   -a3c        |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|   0 0 0 0 0 0         0 0 0 0 0 0 0 0 0 0 0 0 0 0 -b2 -ac -bd -c2 a4 0  0  0|
|d2 0 0 0 0 0 -bc3+ac2d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c   d   0   0   0  a4 0  0|
|   0 0 0 0 0 -b3d+a2cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a   b   -c  -d  0  0  a4 0|
|   0 0 0 0 0 b4-a2bc   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0   0   a   b   0  0  0  a|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  a3b 0   0   0   a3c 0   0   0   a3d 0   0   0   a2b2 0    0    0    a2bc 0 |
|  0   a3b 0   0   0   a3c 0   0   0   a3d 0   0   0    a2b2 0    0    0    a2|
|  0   0   a3b 0   0   0   a3c 0   0   0   a3d 0   0    0    a2b2 0    0    0 |
|4 0   0   0   a3b 0   0   0   a3c 0   0   0   a3d 0    0    0    a2b2 0    0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|   0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2|
|bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0   |
|   a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0   |
|   0    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0    0    0    ab3 0   0   0   ab2c 0    0    0    ab2d 0    0    0    abc2 |
| a2d2 0    0    0   ab3 0   0   0    ab2c 0    0    0    ab2d 0    0    0    |
| 0    a2d2 0    0   0   ab3 0   0    0    ab2c 0    0    0    ab2d 0    0    |
| 0    0    a2d2 0   0   0   ab3 0    0    0    ab2c 0    0    0    ab2d 0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0    0    0    abcd 0    0    0    abd2 0    0    0    ac3 0   0   0   ac2d 0|
|abc2 0    0    0    abcd 0    0    0    abd2 0    0    0   ac3 0   0   0    a|
|0    abc2 0    0    0    abcd 0    0    0    abd2 0    0   0   ac3 0   0    0|
|0    0    abc2 0    0    0    abcd 0    0    0    abd2 0   0   0   ac3 0    0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|    0    0    acd2 0    0    0    ad3 0   0   0   b4 0  0  0  b3c 0   0   0  |
|c2d 0    0    0    acd2 0    0    0   ad3 0   0   0  b4 0  0  0   b3c 0   0  |
|    ac2d 0    0    0    acd2 0    0   0   ad3 0   0  0  b4 0  0   0   b3c 0  |
|    0    ac2d 0    0    0    acd2 0   0   0   ad3 0  0  0  b4 0   0   0   b3c|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| b3d 0   0   0   b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0    |
| 0   b3d 0   0   0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    |
| 0   0   b3d 0   0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    |
| 0   0   0   b3d 0    0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|bc3 0   0   0   bc2d 0    0    0    bcd2 0    0    0    bd3 0   0   0   c4 0 |
|0   bc3 0   0   0    bc2d 0    0    0    bcd2 0    0    0   bd3 0   0   0  c4|
|0   0   bc3 0   0    0    bc2d 0    0    0    bcd2 0    0   0   bd3 0   0  0 |
|0   0   0   bc3 0    0    0    bc2d 0    0    0    bcd2 0   0   0   bd3 0  0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0  0  c3d 0   0   0   c2d2 0    0    0    cd3 0   0   0   d4 0  0  0  |, {2}|
| 0  0  0   c3d 0   0   0    c2d2 0    0    0   cd3 0   0   0  d4 0  0  |  {3}|
| c4 0  0   0   c3d 0   0    0    c2d2 0    0   0   cd3 0   0  0  d4 0  |  {3}|
| 0  c4 0   0   0   c3d 0    0    0    c2d2 0   0   0   cd3 0  0  0  d4 |  {3}|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| | -b2 -ac -bd -c2 a4 0  0  0  a3b 0   0   0   a3c 0   0   0   a3d 0   0   0 |
| | c   d   0   0   0  a4 0  0  0   a3b 0   0   0   a3c 0   0   0   a3d 0   0 |
| | a   b   -c  -d  0  0  a4 0  0   0   a3b 0   0   0   a3c 0   0   0   a3d 0 |
| | 0   0   a   b   0  0  0  a4 0   0   0   a3b 0   0   0   a3c 0   0   0   a3|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    |
|  0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    |
|  0    0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    a2c2 |
|d 0    0    0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0    a2cd 0    0    0    a2d2 0    0    0    ab3 0   0   0   ab2c 0    0    0|
|0    0    a2cd 0    0    0    a2d2 0    0    0   ab3 0   0   0    ab2c 0    0|
|0    0    0    a2cd 0    0    0    a2d2 0    0   0   ab3 0   0    0    ab2c 0|
|a2c2 0    0    0    a2cd 0    0    0    a2d2 0   0   0   ab3 0    0    0    a|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0    abd2 0    0  |
|    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0    abd2 0  |
|    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0    abd|
|b2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  0    ac3 0   0   0   ac2d 0    0    0    acd2 0    0    0    ad3 0   0   0 |
|  0    0   ac3 0   0   0    ac2d 0    0    0    acd2 0    0    0   ad3 0   0 |
|2 0    0   0   ac3 0   0    0    ac2d 0    0    0    acd2 0    0   0   ad3 0 |
|  abd2 0   0   0   ac3 0    0    0    ac2d 0    0    0    acd2 0   0   0   ad|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  b4 0  0  0  b3c 0   0   0   b3d 0   0   0   b2c2 0    0    0    b2cd 0    0|
|  0  b4 0  0  0   b3c 0   0   0   b3d 0   0   0    b2c2 0    0    0    b2cd 0|
|  0  0  b4 0  0   0   b3c 0   0   0   b3d 0   0    0    b2c2 0    0    0    b|
|3 0  0  0  b4 0   0   0   b3c 0   0   0   b3d 0    0    0    b2c2 0    0    0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|    0    b2d2 0    0    0    bc3 0   0   0   bc2d 0    0    0    bcd2 0    0 |
|    0    0    b2d2 0    0    0   bc3 0   0   0    bc2d 0    0    0    bcd2 0 |
|2cd 0    0    0    b2d2 0    0   0   bc3 0   0    0    bc2d 0    0    0    bc|
|    b2cd 0    0    0    b2d2 0   0   0   bc3 0    0    0    bc2d 0    0    0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|   0    bd3 0   0   0   c4 0  0  0  c3d 0   0   0   c2d2 0    0    0    cd3 0|
|   0    0   bd3 0   0   0  c4 0  0  0   c3d 0   0   0    c2d2 0    0    0   c|
|d2 0    0   0   bd3 0   0  0  c4 0  0   0   c3d 0   0    0    c2d2 0    0   0|
|   bcd2 0   0   0   bd3 0  0  0  c4 0   0   0   c3d 0    0    0    c2d2 0   0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-------------------------+---------------------------------------------------|
|   0   0   d4 0  0  0  |)|subquotient ({4} | ad  bd  cd  d2  a2d  0 0 -abd 0 |
|d3 0   0   0  d4 0  0  | |             {4} | -ac -bc -c2 -cd -a2c 0 0 abc  0 |
|   cd3 0   0  0  d4 0  | |             {4} | -ab -b2 -bc -bd -a2b 0 0 ab2  0 |
|   0   cd3 0  0  0  d4 | |             {4} | a2  ab  ac  ad  a3   0 0 -a2b 0 |
|                         |                                                   |
|                         |{-2, 4}                                            |
|-------------------------+---------------------------------------------------|
|                         |subquotient ({2} | 0 ab2 abd abd 0 a2c a2c ac2 ab2 |
|                         |             {3} | 0 -ac 0   0   0 -ad -ad 0   -ac |
|                         |             {3} | 0 -a2 ac  ac  0 -ab -ab ad  -a2 |
|                         |             {3} | 0 0   -a2 -a2 0 0   0   -ab 0   |
|                         |                                                   |
|                         |{-2, 3}                                            |
|-------------------------+---------------------------------------------------|
|                         |subquotient (| a2 ab ac ad b2 bc bd c2 cd d2 bc-ad |
|                         |                                                   |
|                         |{-2, 2}                                            |
|                         |                                                   |
|                         |                                                   |
|                         |                                                   |
|-------------------------+---------------------------------------------------|
|                         |0                                                  |
|                         |                                                   |
|                         |{-2, 1}                                            |
|                         |                                                   |
|                         |                                                   |
|                         |                                                   |
|-------------------------+---------------------------------------------------|
|                         |0                                                  |
|                         |                                                   |
|                         |{-2, 0}                                            |
|-------------------------+---------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0 0 0 -acd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -b2d -abd 0 0 0 -bcd 0 0 0 0 0 0|
|0 0 0 ac2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b2c  abc  0 0 0 bc2  0 0 0 0 0 0|
|0 0 0 abc  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b3   ab2  0 0 0 b2c  0 0 0 0 0 0|
|0 0 0 -a2c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -ab2 -a2b 0 0 0 -abc 0 0 0 0 0 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b3  b2d b2d abd abc abc abc bc2 bc2 ac2 b2c b2c bcd bcd bcd 0     bd2 c3  0 b|
|-bc 0   0   0   -bd -bd -bd 0   0   0   -c2 -c2 0   0   0   cd    0   0   0 0|
|-ab bc  bc  ac  -b2 -b2 -b2 bd  bd  ad  -ac -ac c2  c2  c2  bc+ad cd  cd  0 c|
|0   -ab -ab -a2 0   0   0   -b2 -b2 -ab 0   0   -ac -ac -ac -ab   -ad -bc 0 -|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b3-a2c ac2-b2d c3-bd2 a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3 b2c b2d bc2 b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0 0 0 0 0 0 0 0 0 0 0 -c2d -bcd -acd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
| 0 0 0 0 0 0 0 0 0 0 0 c3   bc2  ac2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
| 0 0 0 0 0 0 0 0 0 0 0 bc2  b2c  abc  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
| 0 0 0 0 0 0 0 0 0 0 0 -ac2 -abc -a2c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2 0 acd acd acd c2d c2d 0 0 0        0        0 0 0 0 0 0 0 0 0 0 0 0 0 0   |
|   0 -d2 -d2 -d2 0   0   0 0 -acd     -acd     0 0 0 0 0 0 0 0 0 0 0 0 0 -ac2|
|d  0 -bd -bd -bd d2  d2  0 0 -abc-a2d -abc-a2d 0 0 0 0 0 0 0 0 0 0 0 0 0 b3-a|
|ad 0 0   0   0   -bd -bd 0 0 a2b      a2b      0 0 0 0 0 0 0 0 0 0 0 0 0 0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|cd bd2 c3 c2d cd2 d3 |, | bc-ad b3-a2c ac2-b2d c3-bd2 a3 a2b a2c a2d ab2 abc |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0 0 d  a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0|
| 0 0 -c 0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0|
| 0 0 -b 0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   a|
| 0 0 a  0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|     0 0        0        0 0 0 0 0 0 0       0 0 0 0 0 0 0 0 -b2 -ac -bd -c2 |
|+b2d 0 -bcd     -bcd     0 0 0 0 0 0 -c3+bd2 0 0 0 0 0 0 0 0 c   d   0   0   |
|2c   0 -b2c-abd -b2c-abd 0 0 0 0 0 0 0       0 0 0 0 0 0 0 0 a   b   -c  -d  |
|     0 ab2      ab2      0 0 0 0 0 0 b3-a2c  0 0 0 0 0 0 0 0 0   0   a   b   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|abd ac2 acd ad2 b3 b2c b2d bc2 bcd bd2 c3 c2d cd2 d3 |)                      |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0 |
|   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad|
|b2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0 |
|   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   a|
|0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0|
|0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0|
|0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0  |
|2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd|
|  ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0  |
|  0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0 |
|   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0 |
|   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0 |
|   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0   0   d3 0  0 |
| 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0   0   0  d3 0 |
| bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2 0   0  0  d3|
| 0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0   cd2 0  0  0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0  |
|  0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0  |
|  0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0  |
|2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0  |, {4} | d  a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   a|
| 0  |  {4} | -c 0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0|
| 0  |  {4} | -b 0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0|
| d3 |  {4} | a  0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   a2d 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0   0   d3 0  0  0  |, {|
| 0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0   0   0  d3 0  0  |  {|
| 0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2 0   0  0  d3 0  |  {|
| 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0   cd2 0  0  0  d3 |  {|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|b2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0 |
|   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0 |
|   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0 |
|   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   ac|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2} | -b2 -ac -bd -c2 a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   |
|3} | c   d   0   0   0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   |
|3} | a   b   -c  -d  0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d |
|3} | 0   0   a   b   0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0   0  |
|  0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0   0  |
|  0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc2 0  |
|d 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0   bc2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0|
|0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0|
|0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   a|
|a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0   0   |
| 0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0   0   |
| 0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2 0   |
| 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0   cd2 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0 |
|   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0 |
|cd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc|
|   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d3 0  0  0  |)                                                               |
|0  d3 0  0  |                                                                |
|0  0  d3 0  |                                                                |
|0  0  0  d3 |                                                                |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0  |
|  0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0  |
|2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2|
|  bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-------------------+---------------------------------------------------------|
|                   |subquotient ({5} | 0 0 0 0 0 0 a2 ab ac ad b2 bc bd c2 cd|
|                   |                                                         |
|                   |{-1, 4}                                                  |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|-------------------+---------------------------------------------------------|
| 0   d3 0  0  0  |)|subquotient ({4} | d  ad  0 0 -bd 0 0 0 0 -cd 0 0 0 0 0 0|
| 0   0  d3 0  0  | |             {4} | -c -ac 0 0 bc  0 0 0 0 c2  0 0 0 0 0 0|
| 0   0  0  d3 0  | |             {4} | -b -ab 0 0 b2  0 0 0 0 bc  0 0 0 0 0 0|
| cd2 0  0  0  d3 | |             {4} | a  a2  0 0 -ab 0 0 0 0 -ac 0 0 0 0 0 0|
|                   |                                                         |
|                   |{-1, 3}                                                  |
|-------------------+---------------------------------------------------------|
|                   |subquotient ({2} | 0 0 b2 bd 0 bd 0 ac ac c2 0 0 0      0|
|                   |             {3} | 0 0 -c 0  0 0  0 -d -d 0  0 0 -cd    -|
|                   |             {3} | 0 0 -a c  0 c  0 -b -b d  0 0 -bc-ad -|
|                   |             {3} | 0 0 0  -a 0 -a 0 0  0  -b 0 0 ab     a|
|                   |                                                         |
|                   |{-1, 2}                                                  |
|-------------------+---------------------------------------------------------|
|                   |subquotient (| a b c d bc-ad b3-a2c ac2-b2d c3-bd2 a2 ab |
|                   |                                                         |
|                   |{-1, 1}                                                  |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|-------------------+---------------------------------------------------------|
|                   |0                                                        |
|                   |                                                         |
|                   |{-1, 0}                                                  |
|-------------------+---------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| d2 |, {5} | a2 ab ac ad b2 bc bd c2 cd d2 |)                                |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0 0 0 0 0 0 0 0 0 d  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0|
| 0 0 0 0 0 0 0 0 0 -c 0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0|
| 0 0 0 0 0 0 0 0 0 -b 0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b|
| 0 0 0 0 0 0 0 0 0 a  0  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|      0 0 0 0 0 0 0 0 0 0 0 0 0 -b2 -ac -bd -c2 a2 0  0  0  ab 0  0  0  ac 0 |
|cd    0 0 0 0 0 0 0 0 0 0 0 0 0 c   d   0   0   0  a2 0  0  0  ab 0  0  0  ac|
|bc-ad 0 0 0 0 0 0 0 0 0 0 0 0 0 a   b   -c  -d  0  0  a2 0  0  0  ab 0  0  0 |
|b     0 0 0 0 0 0 0 0 0 0 0 0 0 0   0   a   b   0  0  0  a2 0  0  0  ab 0  0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|ac ad b2 bc bd c2 cd d2 |, | bc-ad b3-a2c ac2-b2d c3-bd2 a2 ab ac ad b2 bc bd|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |, {4} | d  |
|  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |  {4} | -c |
|2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |  {4} | -b |
|  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |  {4} | a  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0|
| 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0|
| ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0|
| 0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  c|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| c2 cd d2 |)                                                                 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0 |
|0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd|
|0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0 |
|0  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  d2 0  0  0  |, {2} | -b2 -ac -bd -c2 a2 0  0  0  ab 0  0  0  ac 0  0  0  ad|
|  0  d2 0  0  |  {3} | c   d   0   0   0  a2 0  0  0  ab 0  0  0  ac 0  0  0 |
|  0  0  d2 0  |  {3} | a   b   -c  -d  0  0  a2 0  0  0  ab 0  0  0  ac 0  0 |
|d 0  0  0  d2 |  {3} | 0   0   a   b   0  0  0  a2 0  0  0  ab 0  0  0  ac 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |)                                |
| 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |                                 |
| bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |                                 |
| 0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |                                 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0|
| ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0|
| 0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d|
| 0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-------+---------------------------------------------------------------------|
|       |0                                                                    |
|       |                                                                     |
|       |{0, 4}                                                               |
|       |                                                                     |
|       |                                                                     |
|       |                                                                     |
|-------+---------------------------------------------------------------------|
|       |subquotient ({5} | a b c d |, {5} | a b c d |)                       |
|       |                                                                     |
|       |{0, 3}                                                               |
|       |                                                                     |
|       |                                                                     |
|       |                                                                     |
|-------+---------------------------------------------------------------------|
|  0  |)|subquotient ({4} | d  d  a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 |, {4} | d  |
|  0  | |             {4} | -c -c 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 |  {4} | -c |
|2 0  | |             {4} | -b -b 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 |  {4} | -b |
|  d2 | |             {4} | a  a  0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d |  {4} | a  |
|       |                                                                     |
|       |{0, 2}                                                               |
|-------+---------------------------------------------------------------------|
|       |subquotient ({2} | ac b2 c2 bd -b2 -ac -bd -c2 a 0 0 0 b 0 0 0 c 0 0 |
|       |             {3} | -d -c 0  0  c   d   0   0   0 a 0 0 0 b 0 0 0 c 0 |
|       |             {3} | -b -a d  c  a   b   -c  -d  0 0 a 0 0 0 b 0 0 0 c |
|       |             {3} | 0  0  -b -a 0   0   a   b   0 0 0 a 0 0 0 b 0 0 0 |
|       |                                                                     |
|       |{0, 1}                                                               |
|-------+---------------------------------------------------------------------|
|       |cokernel | bc-ad b3-a2c ac2-b2d c3-bd2 a b c d |                     |
|       |                                                                     |
|       |{0, 0}                                                               |
|-------+---------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|---------------------------------------------------------------------+       |
|                                                                     |       |
|                                                                     |       |
|                                                                     |       |
|                                                                     |       |
|                                                                     |       |
|                                                                     |       |
|---------------------------------------------------------------------+       |
|                                                                     |       |
|                                                                     |       |
|                                                                     |       |
|                                                                     |       |
|                                                                     |       |
|                                                                     |       |
|---------------------------------------------------------------------+       |
|a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 |)                                   |       |
|0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 |                                    |       |
|0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 |                                    |       |
|0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d |                                    |       |
|                                                                     |       |
|                                                                     |       |
|---------------------------------------------------------------------+       |
|0 d 0 0 0 |, {2} | -b2 -ac -bd -c2 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 |)|       |
|0 0 d 0 0 |  {3} | c   d   0   0   0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 | |       |
|0 0 0 d 0 |  {3} | a   b   -c  -d  0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 | |       |
|c 0 0 0 d |  {3} | 0   0   a   b   0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d | |       |
|                                                                     |       |
|                                                                     |       |
|---------------------------------------------------------------------+       |
|                                                                     |       |
|                                                                     |       |
|                                                                     |       |
|---------------------------------------------------------------------+       |
+-----------------------------------------------------------------------------+

See also
========

  * SpectralSequence -- the type of all spectral
    sequences
  * SpectralSequencePage -- the type of all
    spectral sequence pages
  * SpectralSequence ^ ZZ -- the kth page of a
    spectral sequence
  * spectralSequence(FilteredComplex)
    -- construct a spectral sequence
    from a filtered complex
  * Examples of filtered complexes and spectral sequences
    -- How to use this package

Ways to use spectralSequence:
=============================

  * spectralSequence(FilteredComplex)
    -- construct a spectral sequence
    from a filtered complex

For the programmer
==================

The object spectralSequence, is a method function with options (Macaulay2Doc).

-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2714:0.

SpectralSequence ^ InfiniteNumber -- the infinity page of a spectral sequence
*****************************************************************************

  * Operator: ^ (Macaulay2Doc),
  * Usage:
        P = E^k
  * Inputs:
      * E, a spectral sequence,
      * k, an infinite number (Macaulay2Doc),
  * Outputs:
      * P, a spectral sequence page,

Description
===========

Returns the infinity page a spectral sequence.

Ways to use this method:
========================

  * SpectralSequence ^ InfiniteNumber,
    -- the infinity page of a spectral sequence
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:3498:0.

SpectralSequence ^ ZZ -- the kth page of a spectral sequence
************************************************************

  * Operator: ^ (Macaulay2Doc),
  * Usage:
        P = E^k
  * Inputs:
      * E, a spectral sequence,
      * k, an integer (Macaulay2Doc),
  * Outputs:
      * P, a spectral sequence page,

Description
===========

Returns the kth page of the spectral sequence.

Consider the filtered complex $K$ below, obtained by multiplying the minimal
free resolution of the rational quartic space curve by successive powers of the
irrelevant ideal.

+----------------------------------------------------+
|i1 : B = QQ[a..d];                                  |
+----------------------------------------------------+
|i2 : J = ideal vars B;                              |
|                                                    |
|o2 : Ideal of B                                     |
+----------------------------------------------------+
|i3 : C = complete res monomialCurveIdeal(B,{1,3,4});|
+----------------------------------------------------+
|i4 : K = filteredComplex(J,C,4);                    |
+----------------------------------------------------+

Let $E$ be the spectral sequence determined by $K$.

+----------------------------+
|i5 : E = spectralSequence K;|
+----------------------------+

We now compute some pages.

+-----------------------------------------------------------------------------+
|i6 : E^0                                                                     |
|                                                                             |
|     +-----------------------------------------------------------------------|
|o6 = |image | a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab2d abc2|
|     |                                                                       |
|     |{-4, 4}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 3}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 2}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 1}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 0}                                                                |
|     +-----------------------------------------------------------------------|
|                                                                             |
|o6 : SpectralSequencePage                                                    |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 bd3 c4 c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|--------------------------+--------------------------------------------------|
|3d c2d2 cd3 d4 0 0 0 0 0 ||subquotient ({2} | a3 0  0  0  a2b 0   0   0   a2c|
|                          |             {3} | 0  a3 0  0  0   a2b 0   0   0  |
|                          |             {3} | 0  0  a3 0  0   0   a2b 0   0  |
|                          |             {3} | 0  0  0  a3 0   0   0   a2b 0  |
|                          |                                                  |
|                          |{-3, 4}                                           |
|--------------------------+--------------------------------------------------|
|                          |subquotient (| a3 a2b a2c a2d ab2 abc abd ac2 acd |
|                          |                                                  |
|                          |{-3, 3}                                           |
|                          |                                                  |
|                          |                                                  |
|                          |                                                  |
|--------------------------+--------------------------------------------------|
|                          |0                                                 |
|                          |                                                  |
|                          |{-3, 2}                                           |
|                          |                                                  |
|                          |                                                  |
|                          |                                                  |
|--------------------------+--------------------------------------------------|
|                          |0                                                 |
|                          |                                                  |
|                          |{-3, 1}                                           |
|                          |                                                  |
|                          |                                                  |
|                          |                                                  |
|--------------------------+--------------------------------------------------|
|                          |0                                                 |
|                          |                                                  |
|                          |{-3, 0}                                           |
|--------------------------+--------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   |
| a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   |
| 0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   |
| 0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|ad2 b3 b2c b2d bc2 bcd bd2 c3 c2d cd2 d3 a4bc-a5d a4b3-a6c a5c2-a4b2d a4c3-a4|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|ac2 0   0   0   acd 0   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b|
|0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0|
|0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0|
|0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bd2 a3b2c-a4bd a3b4-a5bc a4bc2-a3b3d a3bc3-a3b2d2 a3bc2-a4cd a3b3c-a5c2 a4c3-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2|
|   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0 |
|   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0 |
|   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a3b2cd a3c4-a3bcd2 a3bcd-a4d2 a3b3d-a5cd a4c2d-a3b2d2 a3c3d-a3bd3 a2b3c-a3b2d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d 0   0   0   cd2 0   0   0   d3 0  0  0  -a4b2 -a5c -a4bd -a4c2 -a3b3 -a4bc |
|  c2d 0   0   0   cd2 0   0   0  d3 0  0  a4c   a4d  0     0     a3bc  a3bd  |
|  0   c2d 0   0   0   cd2 0   0  0  d3 0  a5    a4b  -a4c  -a4d  a4b   a3b2  |
|  0   0   c2d 0   0   0   cd2 0  0  0  d3 0     0    a5    a4b   0     0     |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| a2b5-a4b2c a3b2c2-a2b4d a2b2c3-a2b3d2 a2b2c2-a3bcd a2b4c-a4bc2 a3bc3-a2b3cd |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-a3b2d -a3bc2 -a3b2c -a4c2 -a3bcd -a3c3 -a3b2d -a4cd -a3bd2 -a3c2d -a2b4 -a3b|
|0      0      a3c2   a3cd  0      0     a3cd   a3d2  0      0      a2b2c a2b2|
|-a3bc  -a3bd  a4c    a3bc  -a3c2  -a3cd a4d    a3bd  -a3cd  -a3d2  a3b2  a2b3|
|a4b    a3b2   0      0     a4c    a3bc  0      0     a4d    a3bd   0     0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a2bc4-a2b2cd2 a2b2cd-a3bd2 a2b4d-a4bcd a3bc2d-a2b3d2 a2bc3d-a2b2d3 a2bc3-a3c2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2c -a2b3d -a2b2c2 -a2b3c -a3bc2 -a2b2cd -a2bc3 -a2b3d -a3bcd -a2b2d2 -a2bc2d |
|d  0      0       a2bc2  a2bcd  0       0      a2bcd  a2bd2  0       0       |
|   -a2b2c -a2b2d  a3bc   a2b2c  -a2bc2  -a2bcd a3bd   a2b2d  -a2bcd  -a2bd2  |
|   a3b2   a2b3    0      0      a3bc    a2b2c  0      0      a3bd    a2b2d   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d a2b3c2-a4c3 a3c4-a2b2c2d a2c5-a2bc2d2 a2bc2d-a3cd2 a2b3cd-a4c2d a3c3d-a2b2c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-a2b2c2 -a3c3 -a2bc2d -a2c4  -a2b2cd -a3c2d -a2bcd2 -a2c3d -a2b2d2 -a3cd2 -a2|
|a2c3    a2c2d 0       0      a2c2d   a2cd2  0       0      a2cd2   a2d3   0  |
|a3c2    a2bc2 -a2c3   -a2c2d a3cd    a2bcd  -a2c2d  -a2cd2 a3d2    a2bd2  -a2|
|0       0     a3c2    a2bc2  0       0      a3cd    a2bcd  0       0      a3d|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2 a2c4d-a2bcd3 a2bcd2-a3d3 a2b3d2-a4cd2 a3c2d2-a2b2d3 a2c3d2-a2bd4 ab4c-a2b3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|bd3 -a2c2d2 -ab5 -a2b3c -ab4d -ab3c2 -ab4c -a2b2c2 -ab3cd -ab2c3 -ab4d -a2b2c|
|    0       ab3c ab3d   0     0      ab2c2 ab2cd   0      0      ab2cd ab2d2 |
|cd2 -a2d3   a2b3 ab4    -ab3c -ab3d  a2b2c ab3c    -ab2c2 -ab2cd a2b2d ab3d  |
|2   a2bd2   0    0      a2b3  ab4    0     0       a2b2c  ab3c   0     0     |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d ab6-a3b3c a2b3c2-ab5d ab3c3-ab4d2 ab3c2-a2b2cd ab5c-a3b2c2 a2b2c3-ab4cd ab2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d -ab3d2 -ab2c2d -ab3c2 -a2bc3 -ab2c2d -abc4  -ab3cd -a2bc2d -ab2cd2 -abc3d -|
|  0      0       abc3   abc2d  0       0      abc2d  abcd2   0       0      a|
|  -ab2cd -ab2d2  a2bc2  ab2c2  -abc3   -abc2d a2bcd  ab2cd   -abc2d  -abcd2 a|
|  a2b2d  ab3d    0      0      a2bc2   ab2c2  0      0       a2bcd   ab2cd  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c4-ab3cd2 ab3cd-a2b2d2 ab5d-a3b2cd a2b2c2d-ab4d2 ab2c3d-ab3d3 ab2c3-a2bc2d ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|ab3d2 -a2bcd2 -ab2d3 -abc2d2 -ab2c3 -a2c4 -abc3d -ac5  -ab2c2d -a2c3d -abc2d2|
|bcd2  abd3    0      0       ac4    ac3d  0      0     ac3d    ac2d2  0      |
|2bd2  ab2d2   -abcd2 -abd3   a2c3   abc3  -ac4   -ac3d a2c2d   abc2d  -ac3d  |
|      0       a2bd2  ab2d2   0      0     a2c3   abc3  0       0      a2c2d  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|4c2-a3bc3 a2bc4-ab3c2d abc5-ab2c2d2 ab2c2d-a2bcd2 ab4cd-a3bc2d a2bc3d-ab3cd2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| -ac4d  -ab2cd2 -a2c2d2 -abcd3 -ac3d2 -ab2d3 -a2cd3 -abd4 -ac2d3 -b6 -ab4c -b|
| 0      ac2d2   acd3    0      0      acd3   ad4    0     0      b4c b4d   0 |
| -ac2d2 a2cd2   abcd2   -ac2d2 -acd3  a2d3   abd3   -acd3 -ad4   ab4 b5    -b|
| abc2d  0       0       a2cd2  abcd2  0      0      a2d3  abd3   0   0     ab|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|abc4d-ab2cd3 ab2cd2-a2bd3 ab4d2-a3bcd2 a2bc2d2-ab3d3 abc3d2-ab2d4 abc4-a2c3d |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|5d -b4c2 -b5c -ab3c2 -b4cd -b3c3 -b5d -ab3cd -b4d2 -b3c2d -b4c2 -ab2c3 -b3c2d|
|   0     b3c2 b3cd   0     0     b3cd b3d2   0     0      b2c3  b2c2d  0     |
|4c -b4d  ab3c b4c    -b3c2 -b3cd ab3d b4d    -b3cd -b3d2  ab2c2 b3c2   -b2c3 |
|4  b5    0    0      ab3c  b4c   0    0      ab3d  b4d    0     0      ab2c2 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|ab3c3-a3c4 a2c5-ab2c3d ac6-abc3d2 abc3d-a2c2d2 ab3c2d-a3c3d a2c4d-ab2c2d2 ac5|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| -b2c4  -b4cd -ab2c2d -b3cd2 -b2c3d -b4d2 -ab2cd2 -b3d3  -b2c2d2 -b3c3 -abc4 |
| 0      b2c2d b2cd2   0      0      b2cd2 b2d3    0      0       bc4   bc3d  |
| -b2c2d ab2cd b3cd    -b2c2d -b2cd2 ab2d2 b3d2    -b2cd2 -b2d3   abc3  b2c3  |
| b3c2   0     0       ab2cd  b3cd   0     0       ab2d2  b3d2    0     0     |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d-abc2d3 abc2d2-a2cd3 ab3cd2-a3c2d2 a2c3d2-ab2cd3 ac4d2-abcd4 abcd3-a2d4 ab3d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-b2c3d -bc5  -b3c2d -abc3d -b2c2d2 -bc4d  -b3cd2 -abc2d2 -b2cd3 -bc3d2 -b3d3 |
|0      0     bc3d   bc2d2  0       0      bc2d2  bcd3    0      0      bcd3  |
|-bc4   -bc3d abc2d  b2c2d  -bc3d   -bc2d2 abcd2  b2cd2   -bc2d2 -bcd3  abd3  |
|abc3   b2c3  0      0      abc2d   b2c2d  0      0       abcd2  b2cd2  0     |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3-a3cd3 a2c2d3-ab2d4 ac3d3-abd5 b5c-ab4d b7-a2b4c ab4c2-b6d b4c3-b5d2 b4c2-ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-abcd3 -b2d4 -bc2d3 -b2c4 -ac5 -bc4d -c6  -b2c3d -ac4d -bc3d2 -c5d  -b2c2d2 -|
|bd4    0     0      c5    c4d  0     0    c4d    c3d2  0      0     c3d2    c|
|b2d3   -bcd3 -bd4   ac4   bc4  -c5   -c4d ac3d   bc3d  -c4d   -c3d2 ac2d2   b|
|0      abd3  b2d3   0     0    ac4   bc4  0      0     ac3d   bc3d  0       0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3cd b6c-a2b3c2 ab3c3-b5cd b3c4-b4cd2 b4cd-ab3d2 b6d-a2b3cd ab3c2d-b5d2 b3c3d-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|ac3d2 -bc2d3 -c4d2 -b2cd3 -ac2d3 -bcd4 -c3d3 -b2d4 -acd4 -bd5 -c2d4 a4 0  0  |
|2d3   0      0     c2d3   cd4    0     0     cd4   d5    0    0     0  a4 0  |
|c2d2  -c3d2  -c2d3 acd3   bcd3   -c2d3 -cd4  ad4   bd4   -cd4 -d5   0  0  a4 |
|      ac2d2  bc2d2 0      0      acd3  bcd3  0     0     ad4  bd4   0  0  0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b4d3 b3c3-ab2c2d b5c2-a2b2c3 ab2c4-b4c2d b2c5-b3c2d2 b3c2d-ab2cd2 b5cd-a2b2c2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0  a3b 0   0   0   a3c 0   0   0   a3d 0   0   0   a2b2 0    0    0    a2bc 0|
|0  0   a3b 0   0   0   a3c 0   0   0   a3d 0   0   0    a2b2 0    0    0    a|
|0  0   0   a3b 0   0   0   a3c 0   0   0   a3d 0   0    0    a2b2 0    0    0|
|a4 0   0   0   a3b 0   0   0   a3c 0   0   0   a3d 0    0    0    a2b2 0    0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d ab2c3d-b4cd2 b2c4d-b3cd3 b3cd2-ab2d3 b5d2-a2b2cd2 ab2c2d2-b4d3 b2c3d2-b3d4 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d|
|2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0  |
|    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0  |
|    0    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b2c4-abc3d b4c3-a2bc4 abc5-b3c3d bc6-b2c3d2 b2c3d-abc2d2 b4c2d-a2bc3d abc4d-b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2 0    0    0    ab3 0   0   0   ab2c 0    0    0    ab2d 0    0    0    abc2|
|  a2d2 0    0    0   ab3 0   0   0    ab2c 0    0    0    ab2d 0    0    0   |
|  0    a2d2 0    0   0   ab3 0   0    0    ab2c 0    0    0    ab2d 0    0   |
|  0    0    a2d2 0   0   0   ab3 0    0    0    ab2c 0    0    0    ab2d 0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3c2d2 bc5d-b2c2d3 b2c2d2-abcd3 b4cd2-a2bc2d2 abc3d2-b3cd3 bc4d2-b2cd4 b2cd3-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0    0    0    abcd 0    0    0    abd2 0    0    0    ac3 0   0   0   ac2d |
| abc2 0    0    0    abcd 0    0    0    abd2 0    0    0   ac3 0   0   0    |
| 0    abc2 0    0    0    abcd 0    0    0    abd2 0    0   0   ac3 0   0    |
| 0    0    abc2 0    0    0    abcd 0    0    0    abd2 0   0   0   ac3 0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bd4 b4d3-a2bcd3 abc2d3-b3d4 bc3d3-b2d5 bc5-ac4d b3c4-a2c5 ac6-b2c4d c7-bc4d2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0    0    0    acd2 0    0    0    ad3 0   0   0   b4 0  0  0  b3c 0   0   0 |
|ac2d 0    0    0    acd2 0    0    0   ad3 0   0   0  b4 0  0  0   b3c 0   0 |
|0    ac2d 0    0    0    acd2 0    0   0   ad3 0   0  0  b4 0  0   0   b3c 0 |
|0    0    ac2d 0    0    0    acd2 0   0   0   ad3 0  0  0  b4 0   0   0   b3|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bc4d-ac3d2 b3c3d-a2c4d ac5d-b2c3d2 c6d-bc3d3 bc3d2-ac2d3 b3c2d2-a2c3d2 ac4d2-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  b3d 0   0   0   b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0   |
|  0   b3d 0   0   0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0   |
|  0   0   b3d 0   0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0   |
|c 0   0   0   b3d 0    0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b2c2d3 c5d2-bc2d4 bc2d3-acd4 b3cd3-a2c2d3 ac3d3-b2cd4 c4d3-bcd5 bcd4-ad5 b3d4|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| bc3 0   0   0   bc2d 0    0    0    bcd2 0    0    0    bd3 0   0   0   c4 0|
| 0   bc3 0   0   0    bc2d 0    0    0    bcd2 0    0    0   bd3 0   0   0  c|
| 0   0   bc3 0   0    0    bc2d 0    0    0    bcd2 0    0   0   bd3 0   0  0|
| 0   0   0   bc3 0    0    0    bc2d 0    0    0    bcd2 0   0   0   bd3 0  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-a2cd4 ac2d4-b2d5 c3d4-bd6 a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  0  0  c3d 0   0   0   c2d2 0    0    0    cd3 0   0   0   d4 0  0  0  |, {2|
|4 0  0  0   c3d 0   0   0    c2d2 0    0    0   cd3 0   0   0  d4 0  0  |  {3|
|  c4 0  0   0   c3d 0   0    0    c2d2 0    0   0   cd3 0   0  0  d4 0  |  {3|
|  0  c4 0   0   0   c3d 0    0    0    c2d2 0   0   0   cd3 0  0  0  d4 |  {3|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b2c ab2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|} | -a4b2 -a5c -a4bd -a4c2 -a3b3 -a4bc -a3b2d -a3bc2 -a3b2c -a4c2 -a3bcd -a3c|
|} | a4c   a4d  0     0     a3bc  a3bd  0      0      a3c2   a3cd  0      0   |
|} | a5    a4b  -a4c  -a4d  a4b   a3b2  -a3bc  -a3bd  a4c    a3bc  -a3c2  -a3c|
|} | 0     0    a5    a4b   0     0     a4b    a3b2   0      0     a4c    a3bc|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bcd2 bd3 c4 c3d c2d2 cd3 d4 |, | a4bc-a5d a4b3-a6c a5c2-a4b2d a4c3-a4bd2 a3b2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|3 -a3b2d -a4cd -a3bd2 -a3c2d -a2b4 -a3b2c -a2b3d -a2b2c2 -a2b3c -a3bc2 -a2b2c|
|  a3cd   a3d2  0      0      a2b2c a2b2d  0      0       a2bc2  a2bcd  0     |
|d a4d    a3bd  -a3cd  -a3d2  a3b2  a2b3   -a2b2c -a2b2d  a3bc   a2b2c  -a2bc2|
|  0      0     a4d    a3bd   0     0      a3b2   a2b3    0      0      a3bc  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c-a4bd a3b4-a5bc a4bc2-a3b3d a3bc3-a3b2d2 a3bc2-a4cd a3b3c-a5c2 a4c3-a3b2cd a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d -a2bc3 -a2b3d -a3bcd -a2b2d2 -a2bc2d -a2b2c2 -a3c3 -a2bc2d -a2c4  -a2b2cd -|
|  0      a2bcd  a2bd2  0       0       a2c3    a2c2d 0       0      a2c2d   a|
|  -a2bcd a3bd   a2b2d  -a2bcd  -a2bd2  a3c2    a2bc2 -a2c3   -a2c2d a3cd    a|
|  a2b2c  0      0      a3bd    a2b2d   0       0     a3c2    a2bc2  0       0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3c4-a3bcd2 a3bcd-a4d2 a3b3d-a5cd a4c2d-a3b2d2 a3c3d-a3bd3 a2b3c-a3b2d a2b5-a4|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|a3c2d -a2bcd2 -a2c3d -a2b2d2 -a3cd2 -a2bd3 -a2c2d2 -ab5 -a2b3c -ab4d -ab3c2 -|
|2cd2  0       0      a2cd2   a2d3   0      0       ab3c ab3d   0     0      a|
|2bcd  -a2c2d  -a2cd2 a3d2    a2bd2  -a2cd2 -a2d3   a2b3 ab4    -ab3c -ab3d  a|
|      a3cd    a2bcd  0       0      a3d2   a2bd2   0    0      a2b3  ab4    0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b2c a3b2c2-a2b4d a2b2c3-a2b3d2 a2b2c2-a3bcd a2b4c-a4bc2 a3bc3-a2b3cd a2bc4-a2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|ab4c -a2b2c2 -ab3cd -ab2c3 -ab4d -a2b2cd -ab3d2 -ab2c2d -ab3c2 -a2bc3 -ab2c2d|
|b2c2 ab2cd   0      0      ab2cd ab2d2   0      0       abc3   abc2d  0      |
|2b2c ab3c    -ab2c2 -ab2cd a2b2d ab3d    -ab2cd -ab2d2  a2bc2  ab2c2  -abc3  |
|     0       a2b2c  ab3c   0     0       a2b2d  ab3d    0      0      a2bc2  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b2cd2 a2b2cd-a3bd2 a2b4d-a4bcd a3bc2d-a2b3d2 a2bc3d-a2b2d3 a2bc3-a3c2d a2b3c2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| -abc4  -ab3cd -a2bc2d -ab2cd2 -abc3d -ab3d2 -a2bcd2 -ab2d3 -abc2d2 -ab2c3 -a|
| 0      abc2d  abcd2   0       0      abcd2  abd3    0      0       ac4    ac|
| -abc2d a2bcd  ab2cd   -abc2d  -abcd2 a2bd2  ab2d2   -abcd2 -abd3   a2c3   ab|
| ab2c2  0      0       a2bcd   ab2cd  0      0       a2bd2  ab2d2   0      0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-a4c3 a3c4-a2b2c2d a2c5-a2bc2d2 a2bc2d-a3cd2 a2b3cd-a4c2d a3c3d-a2b2cd2 a2c4d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2c4 -abc3d -ac5  -ab2c2d -a2c3d -abc2d2 -ac4d  -ab2cd2 -a2c2d2 -abcd3 -ac3d2 |
|3d  0      0     ac3d    ac2d2  0       0      ac2d2   acd3    0      0      |
|c3  -ac4   -ac3d a2c2d   abc2d  -ac3d   -ac2d2 a2cd2   abcd2   -ac2d2 -acd3  |
|    a2c3   abc3  0       0      a2c2d   abc2d  0       0       a2cd2  abcd2  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-a2bcd3 a2bcd2-a3d3 a2b3d2-a4cd2 a3c2d2-a2b2d3 a2c3d2-a2bd4 ab4c-a2b3d ab6-a3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-ab2d3 -a2cd3 -abd4 -ac2d3 -b6 -ab4c -b5d -b4c2 -b5c -ab3c2 -b4cd -b3c3 -b5d |
|acd3   ad4    0     0      b4c b4d   0    0     b3c2 b3cd   0     0     b3cd |
|a2d3   abd3   -acd3 -ad4   ab4 b5    -b4c -b4d  ab3c b4c    -b3c2 -b3cd ab3d |
|0      0      a2d3  abd3   0   0     ab4  b5    0    0      ab3c  b4c   0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b3c a2b3c2-ab5d ab3c3-ab4d2 ab3c2-a2b2cd ab5c-a3b2c2 a2b2c3-ab4cd ab2c4-ab3cd|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-ab3cd -b4d2 -b3c2d -b4c2 -ab2c3 -b3c2d -b2c4  -b4cd -ab2c2d -b3cd2 -b2c3d -b|
|b3d2   0     0      b2c3  b2c2d  0      0      b2c2d b2cd2   0      0      b2|
|b4d    -b3cd -b3d2  ab2c2 b3c2   -b2c3  -b2c2d ab2cd b3cd    -b2c2d -b2cd2 ab|
|0      ab3d  b4d    0     0      ab2c2  b3c2   0     0       ab2cd  b3cd   0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2 ab3cd-a2b2d2 ab5d-a3b2cd a2b2c2d-ab4d2 ab2c3d-ab3d3 ab2c3-a2bc2d ab4c2-a3bc|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|4d2 -ab2cd2 -b3d3  -b2c2d2 -b3c3 -abc4 -b2c3d -bc5  -b3c2d -abc3d -b2c2d2 -bc|
|cd2 b2d3    0      0       bc4   bc3d  0      0     bc3d   bc2d2  0       0  |
|2d2 b3d2    -b2cd2 -b2d3   abc3  b2c3  -bc4   -bc3d abc2d  b2c2d  -bc3d   -bc|
|    0       ab2d2  b3d2    0     0     abc3   b2c3  0      0      abc2d   b2c|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3 a2bc4-ab3c2d abc5-ab2c2d2 ab2c2d-a2bcd2 ab4cd-a3bc2d a2bc3d-ab3cd2 abc4d-ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|4d  -b3cd2 -abc2d2 -b2cd3 -bc3d2 -b3d3 -abcd3 -b2d4 -bc2d3 -b2c4 -ac5 -bc4d -|
|    bc2d2  bcd3    0      0      bcd3  bd4    0     0      c5    c4d  0     0|
|2d2 abcd2  b2cd2   -bc2d2 -bcd3  abd3  b2d3   -bcd3 -bd4   ac4   bc4  -c5   -|
|2d  0      0       abcd2  b2cd2  0     0      abd3  b2d3   0     0    ac4   b|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2cd3 ab2cd2-a2bd3 ab4d2-a3bcd2 a2bc2d2-ab3d3 abc3d2-ab2d4 abc4-a2c3d ab3c3-a3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c6  -b2c3d -ac4d -bc3d2 -c5d  -b2c2d2 -ac3d2 -bc2d3 -c4d2 -b2cd3 -ac2d3 -bcd4|
|    c4d    c3d2  0      0     c3d2    c2d3   0      0     c2d3   cd4    0    |
|c4d ac3d   bc3d  -c4d   -c3d2 ac2d2   bc2d2  -c3d2  -c2d3 acd3   bcd3   -c2d3|
|c4  0      0     ac3d   bc3d  0       0      ac2d2  bc2d2 0      0      acd3 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c4 a2c5-ab2c3d ac6-abc3d2 abc3d-a2c2d2 ab3c2d-a3c3d a2c4d-ab2c2d2 ac5d-abc2d3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| -c3d3 -b2d4 -acd4 -bd5 -c2d4 a4 0  0  0  a3b 0   0   0   a3c 0   0   0   a3d|
| 0     cd4   d5    0    0     0  a4 0  0  0   a3b 0   0   0   a3c 0   0   0  |
| -cd4  ad4   bd4   -cd4 -d5   0  0  a4 0  0   0   a3b 0   0   0   a3c 0   0  |
| bcd3  0     0     ad4  bd4   0  0  0  a4 0   0   0   a3b 0   0   0   a3c 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| abc2d2-a2cd3 ab3cd2-a3c2d2 a2c3d2-ab2cd3 ac4d2-abcd4 abcd3-a2d4 ab3d3-a3cd3 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   0   0   a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    a2c2|
| a3d 0   0   0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0   |
| 0   a3d 0   0    0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0   |
| 0   0   a3d 0    0    0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a2c2d3-ab2d4 ac3d3-abd5 b5c-ab4d b7-a2b4c ab4c2-b6d b4c3-b5d2 b4c2-ab3cd b6c-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0    0    0    a2cd 0    0    0    a2d2 0    0    0    ab3 0   0   0   ab2c |
| a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0    0   ab3 0   0   0    |
| 0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0   0   ab3 0   0    |
| 0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0   0   0   ab3 0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a2b3c2 ab3c3-b5cd b3c4-b4cd2 b4cd-ab3d2 b6d-a2b3cd ab3c2d-b5d2 b3c3d-b4d3 b3c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0    ab|
|ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0 |
|0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0 |
|0    0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3-ab2c2d b5c2-a2b2c3 ab2c4-b4c2d b2c5-b3c2d2 b3c2d-ab2cd2 b5cd-a2b2c2d ab2c3d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d2 0    0    0    ac3 0   0   0   ac2d 0    0    0    acd2 0    0    0    ad3|
|   abd2 0    0    0   ac3 0   0   0    ac2d 0    0    0    acd2 0    0    0  |
|   0    abd2 0    0   0   ac3 0   0    0    ac2d 0    0    0    acd2 0    0  |
|   0    0    abd2 0   0   0   ac3 0    0    0    ac2d 0    0    0    acd2 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-b4cd2 b2c4d-b3cd3 b3cd2-ab2d3 b5d2-a2b2cd2 ab2c2d2-b4d3 b2c3d2-b3d4 b2c4-abc|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   0   0   b4 0  0  0  b3c 0   0   0   b3d 0   0   0   b2c2 0    0    0    |
| ad3 0   0   0  b4 0  0  0   b3c 0   0   0   b3d 0   0   0    b2c2 0    0    |
| 0   ad3 0   0  0  b4 0  0   0   b3c 0   0   0   b3d 0   0    0    b2c2 0    |
| 0   0   ad3 0  0  0  b4 0   0   0   b3c 0   0   0   b3d 0    0    0    b2c2 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3d b4c3-a2bc4 abc5-b3c3d bc6-b2c3d2 b2c3d-abc2d2 b4c2d-a2bc3d abc4d-b3c2d2 bc|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|b2cd 0    0    0    b2d2 0    0    0    bc3 0   0   0   bc2d 0    0    0    b|
|0    b2cd 0    0    0    b2d2 0    0    0   bc3 0   0   0    bc2d 0    0    0|
|0    0    b2cd 0    0    0    b2d2 0    0   0   bc3 0   0    0    bc2d 0    0|
|0    0    0    b2cd 0    0    0    b2d2 0   0   0   bc3 0    0    0    bc2d 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|5d-b2c2d3 b2c2d2-abcd3 b4cd2-a2bc2d2 abc3d2-b3cd3 bc4d2-b2cd4 b2cd3-abd4 b4d3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|cd2 0    0    0    bd3 0   0   0   c4 0  0  0  c3d 0   0   0   c2d2 0    0   |
|    bcd2 0    0    0   bd3 0   0   0  c4 0  0  0   c3d 0   0   0    c2d2 0   |
|    0    bcd2 0    0   0   bd3 0   0  0  c4 0  0   0   c3d 0   0    0    c2d2|
|    0    0    bcd2 0   0   0   bd3 0  0  0  c4 0   0   0   c3d 0    0    0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-a2bcd3 abc2d3-b3d4 bc3d3-b2d5 bc5-ac4d b3c4-a2c5 ac6-b2c4d c7-bc4d2 bc4d-ac3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0    cd3 0   0   0   d4 0  0  0  |)                                         |
| 0    0   cd3 0   0   0  d4 0  0  |                                          |
| 0    0   0   cd3 0   0  0  d4 0  |                                          |
| c2d2 0   0   0   cd3 0  0  0  d4 |                                          |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2 b3c3d-a2c4d ac5d-b2c3d2 c6d-bc3d3 bc3d2-ac2d3 b3c2d2-a2c3d2 ac4d2-b2c2d3 c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|5d2-bc2d4 bc2d3-acd4 b3cd3-a2c2d3 ac3d3-b2cd4 c4d3-bcd5 bcd4-ad5 b3d4-a2cd4 a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2d4-b2d5 c3d4-bd6 a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab2d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 bd3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|----------------------+------------------------------------------------------|
|                      |subquotient ({4} | a2 0  0  0  ab 0  0  0  ac 0  0  0 |
|                      |             {4} | 0  a2 0  0  0  ab 0  0  0  ac 0  0 |
|                      |             {4} | 0  0  a2 0  0  0  ab 0  0  0  ac 0 |
|                      |             {4} | 0  0  0  a2 0  0  0  ab 0  0  0  ac|
|                      |                                                      |
|                      |{-2, 4}                                               |
|----------------------+------------------------------------------------------|
| c4 c3d c2d2 cd3 d4 |)|subquotient ({2} | a2 0  0  0  ab 0  0  0  ac 0  0  0 |
|                      |             {3} | 0  a2 0  0  0  ab 0  0  0  ac 0  0 |
|                      |             {3} | 0  0  a2 0  0  0  ab 0  0  0  ac 0 |
|                      |             {3} | 0  0  0  a2 0  0  0  ab 0  0  0  ac|
|                      |                                                      |
|                      |{-2, 3}                                               |
|----------------------+------------------------------------------------------|
|                      |subquotient (| a2 ab ac ad b2 bc bd c2 cd d2 a3bc-a4d |
|                      |                                                      |
|                      |{-2, 2}                                               |
|                      |                                                      |
|                      |                                                      |
|                      |                                                      |
|----------------------+------------------------------------------------------|
|                      |0                                                     |
|                      |                                                      |
|                      |{-2, 1}                                               |
|                      |                                                      |
|                      |                                                      |
|                      |                                                      |
|----------------------+------------------------------------------------------|
|                      |0                                                     |
|                      |                                                      |
|                      |{-2, 0}                                               |
|----------------------+------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0|
| 0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d|
| 0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0|
| 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0|
| 0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d|
| 0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0|
| 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a3b3-a5c a4c2-a3b2d a3c3-a3bd2 a2b2c-a3bd a2b4-a4bc a3bc2-a2b3d a2bc3-a2b2d2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  0  0  a3d  a2bd  a2cd  a2d2  ab2d  abcd  abd2  ac2d  acd2  ad3   b3d  b2cd |
|2 0  0  -a3c -a2bc -a2c2 -a2cd -ab2c -abc2 -abcd -ac3  -ac2d -acd2 -b3c -b2c2|
|  d2 0  -a3b -a2b2 -a2bc -a2bd -ab3  -ab2c -ab2d -abc2 -abcd -abd2 -b4  -b3c |
|  0  d2 a4   a3b   a3c   a3d   a2b2  a2bc  a2bd  a2c2  a2cd  a2d2  ab3  ab2c |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  0  0  -a3b2 -a4c -a3bd -a3c2 -a2b3 -a3bc -a2b2d -a2bc2 -a2b2c -a3c2 -a2bcd |
|2 0  0  a3c   a3d  0     0     a2bc  a2bd  0      0      a2c2   a2cd  0      |
|  d2 0  a4    a3b  -a3c  -a3d  a3b   a2b2  -a2bc  -a2bd  a3c    a2bc  -a2c2  |
|  0  d2 0     0    a4    a3b   0     0     a3b    a2b2   0      0     a3c    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a2bc2-a3cd a2b3c-a4c2 a3c3-a2b2cd a2c4-a2bcd2 a2bcd-a3d2 a2b3d-a4cd a3c2d-a2b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| b2d2  bc2d  bcd2  bd3   c3d  c2d2  cd3   d4   a3 0  0  0  a2b 0   0   0   a2|
| -b2cd -bc3  -bc2d -bcd2 -c4  -c3d  -c2d2 -cd3 0  a3 0  0  0   a2b 0   0   0 |
| -b3d  -b2c2 -b2cd -b2d2 -bc3 -bc2d -bcd2 -bd3 0  0  a3 0  0   0   a2b 0   0 |
| ab2d  abc2  abcd  abd2  ac3  ac2d  acd2  ad3  0  0  0  a3 0   0   0   a2b 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-a2c3 -a2b2d -a3cd -a2bd2 -a2c2d -ab4 -a2b2c -ab3d -ab2c2 -ab3c -a2bc2 -ab2cd|
|0     a2cd   a2d2  0      0      ab2c ab2d   0     0      abc2  abcd   0     |
|-a2cd a3d    a2bd  -a2cd  -a2d2  a2b2 ab3    -ab2c -ab2d  a2bc  ab2c   -abc2 |
|a2bc  0      0     a3d    a2bd   0    0      a2b2  ab3    0     0      a2bc  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2d2 a2c3d-a2bd3 ab3c-a2b2d ab5-a3b2c a2b2c2-ab4d ab2c3-ab3d2 ab2c2-a2bcd ab4c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0  |
|  a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0  |
|  0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0  |
|  0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| -abc3 -ab3d -a2bcd -ab2d2 -abc2d -ab2c2 -a2c3 -abc2d -ac4  -ab2cd -a2c2d -ab|
| 0     abcd  abd2   0      0      ac3    ac2d  0      0     ac2d   acd2   0  |
| -abcd a2bd  ab2d   -abcd  -abd2  a2c2   abc2  -ac3   -ac2d a2cd   abcd   -ac|
| ab2c  0     0      a2bd   ab2d   0      0     a2c2   abc2  0      0      a2c|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-a3bc2 a2bc3-ab3cd abc4-ab2cd2 ab2cd-a2bd2 ab4d-a3bcd a2bc2d-ab3d2 abc3d-ab2d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| ac2 0   0   0   acd 0   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   |
| 0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   |
| 0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   |
| 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|cd2 -ac3d -ab2d2 -a2cd2 -abd3 -ac2d2 -b5 -ab3c -b4d -b3c2 -b4c -ab2c2 -b3cd -|
|    0     acd2   ad3    0     0      b3c b3d   0    0     b2c2 b2cd   0     0|
|2d  -acd2 a2d2   abd2   -acd2 -ad3   ab3 b4    -b3c -b3d  ab2c b3c    -b2c2 -|
|d   abcd  0      0      a2d2  abd2   0   0     ab3  b4    0    0      ab2c  b|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3 abc3-a2c2d ab3c2-a3c3 a2c4-ab2c2d ac5-abc2d2 abc2d-a2cd2 ab3cd-a3c2d a2c3d-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c|
|0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0|
|0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0|
|0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b2c3 -b4d -ab2cd -b3d2 -b2c2d -b3c2 -abc3 -b2c2d -bc4  -b3cd -abc2d -b2cd2 -b|
|     b2cd b2d2   0     0      bc3   bc2d  0      0     bc2d  bcd2   0      0 |
|b2cd ab2d b3d    -b2cd -b2d2  abc2  b2c2  -bc3   -bc2d abcd  b2cd   -bc2d  -b|
|3c   0    0      ab2d  b3d    0     0     abc2   b2c2  0     0      abcd   b2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|ab2cd2 ac4d-abcd3 abcd2-a2d3 ab3d2-a3cd2 a2c2d2-ab2d3 ac3d2-abd4 b4c-ab3d b6-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2d 0   0   0   cd2 0   0   0   d3 0  0  0  |, {4} | a3d  a2bd  a2cd  a2d2  ab|
|   c2d 0   0   0   cd2 0   0   0  d3 0  0  |  {4} | -a3c -a2bc -a2c2 -a2cd -a|
|   0   c2d 0   0   0   cd2 0   0  0  d3 0  |  {4} | -a3b -a2b2 -a2bc -a2bd -a|
|   0   0   c2d 0   0   0   cd2 0  0  0  d3 |  {4} | a4   a3b   a3c   a3d   a2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c3d -b3d2 -abcd2 -b2d3 -bc2d2 -b2c3 -ac4 -bc3d -c5  -b2c2d -ac3d -bc2d2 -c4d |
|    bcd2  bd3    0     0      c4    c3d  0     0    c3d    c2d2  0      0    |
|cd2 abd2  b2d2   -bcd2 -bd3   ac3   bc3  -c4   -c3d ac2d   bc2d  -c3d   -c2d2|
|cd  0     0      abd2  b2d2   0     0    ac3   bc3  0      0     ac2d   bc2d |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a2b3c ab3c2-b5d b3c3-b4d2 b3c2-ab2cd b5c-a2b2c2 ab2c3-b4cd b2c4-b3cd2 b3cd-ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2d  abcd  abd2  ac2d  acd2  ad3   b3d  b2cd  b2d2  bc2d  bcd2  bd3   c3d  c2d|
|b2c -abc2 -abcd -ac3  -ac2d -acd2 -b3c -b2c2 -b2cd -bc3  -bc2d -bcd2 -c4  -c3|
|b3  -ab2c -ab2d -abc2 -abcd -abd2 -b4  -b3c  -b3d  -b2c2 -b2cd -b2d2 -bc3 -bc|
|b2  a2bc  a2bd  a2c2  a2cd  a2d2  ab3  ab2c  ab2d  abc2  abcd  abd2  ac3  ac2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| -b2cd2 -ac2d2 -bcd3 -c3d2 -b2d3 -acd3 -bd4 -c2d3 a3 0  0  0  a2b 0   0   0  |
| c2d2   cd3    0     0     cd3   d4    0    0     0  a3 0  0  0   a2b 0   0  |
| acd2   bcd2   -c2d2 -cd3  ad3   bd3   -cd3 -d4   0  0  a3 0  0   0   a2b 0  |
| 0      0      acd2  bcd2  0     0     ad3  bd3   0  0  0  a3 0   0   0   a2b|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2d2 b5d-a2b2cd ab2c2d-b4d2 b2c3d-b3d3 b2c3-abc2d b4c2-a2bc3 abc4-b3c2d bc5-b2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2  cd3   d4   a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2|
|d  -c2d2 -cd3 0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0  |
|2d -bcd2 -bd3 0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0  |
|d  acd2  ad3  0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   a2d 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   |
| 0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   |
| 0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd |
| 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2d2 b2c2d-abcd2 b4cd-a2bc2d abc3d-b3cd2 bc4d-b2cd3 b2cd2-abd3 b4d2-a2bcd2 ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   |
| ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   |
| 0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   |
| 0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0|
|0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0|
|0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0|
|abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2d2-b3d3 bc3d2-b2d4 bc4-ac3d b3c3-a2c4 ac5-b2c3d c6-bc3d2 bc3d-ac2d2 b3c2d-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   b|
|0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0|
|0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0|
|0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0   bc2 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0|
|   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0|
|   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0|
|2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2c3d ac4d-b2c2d2 c5d-bc2d3 bc2d2-acd3 b3cd2-a2c2d2 ac3d2-b2cd3 c4d2-bcd4 bcd3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|cd 0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0   0   d3|
|   bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0   0   0 |
|   0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2 0   0 |
|   0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0   cd2 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  c2d 0   0   0   cd2 0   0   0   d3 0  0  0  |, {2} | -a3b2 -a4c -a3bd -a3c2|
|  0   c2d 0   0   0   cd2 0   0   0  d3 0  0  |  {3} | a3c   a3d  0     0    |
|  0   0   c2d 0   0   0   cd2 0   0  0  d3 0  |  {3} | a4    a3b  -a3c  -a3d |
|3 0   0   0   c2d 0   0   0   cd2 0  0  0  d3 |  {3} | 0     0    a4    a3b  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-ad4 b3d3-a2cd3 ac2d3-b2d4 c3d3-bd5 a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0  0  0  |)                                                                 |
| d3 0  0  |                                                                  |
| 0  d3 0  |                                                                  |
| 0  0  d3 |                                                                  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| -a2b3 -a3bc -a2b2d -a2bc2 -a2b2c -a3c2 -a2bcd -a2c3 -a2b2d -a3cd -a2bd2 -a2c|
| a2bc  a2bd  0      0      a2c2   a2cd  0      0     a2cd   a2d2  0      0   |
| a3b   a2b2  -a2bc  -a2bd  a3c    a2bc  -a2c2  -a2cd a3d    a2bd  -a2cd  -a2d|
| 0     0     a3b    a2b2   0      0     a3c    a2bc  0      0     a3d    a2bd|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| b2c b2d bc2 bcd bd2 c3 c2d cd2 d3 |, | a3bc-a4d a3b3-a5c a4c2-a3b2d a3c3-a3b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2d -ab4 -a2b2c -ab3d -ab2c2 -ab3c -a2bc2 -ab2cd -abc3 -ab3d -a2bcd -ab2d2 -ab|
|   ab2c ab2d   0     0      abc2  abcd   0      0     abcd  abd2   0      0  |
|2  a2b2 ab3    -ab2c -ab2d  a2bc  ab2c   -abc2  -abcd a2bd  ab2d   -abcd  -ab|
|   0    0      a2b2  ab3    0     0      a2bc   ab2c  0     0      a2bd   ab2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2 a2b2c-a3bd a2b4-a4bc a3bc2-a2b3d a2bc3-a2b2d2 a2bc2-a3cd a2b3c-a4c2 a3c3-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2d -ab2c2 -a2c3 -abc2d -ac4  -ab2cd -a2c2d -abcd2 -ac3d -ab2d2 -a2cd2 -abd3 |
|    ac3    ac2d  0      0     ac2d   acd2   0      0     acd2   ad3    0     |
|d2  a2c2   abc2  -ac3   -ac2d a2cd   abcd   -ac2d  -acd2 a2d2   abd2   -acd2 |
|d   0      0     a2c2   abc2  0      0      a2cd   abcd  0      0      a2d2  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2b2cd a2c4-a2bcd2 a2bcd-a3d2 a2b3d-a4cd a3c2d-a2b2d2 a2c3d-a2bd3 ab3c-a2b2d a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-ac2d2 -b5 -ab3c -b4d -b3c2 -b4c -ab2c2 -b3cd -b2c3 -b4d -ab2cd -b3d2 -b2c2d |
|0      b3c b3d   0    0     b2c2 b2cd   0     0     b2cd b2d2   0     0      |
|-ad3   ab3 b4    -b3c -b3d  ab2c b3c    -b2c2 -b2cd ab2d b3d    -b2cd -b2d2  |
|abd2   0   0     ab3  b4    0    0      ab2c  b3c   0    0      ab2d  b3d    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b5-a3b2c a2b2c2-ab4d ab2c3-ab3d2 ab2c2-a2bcd ab4c-a3bc2 a2bc3-ab3cd abc4-ab2c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-b3c2 -abc3 -b2c2d -bc4  -b3cd -abc2d -b2cd2 -bc3d -b3d2 -abcd2 -b2d3 -bc2d2 |
|bc3   bc2d  0      0     bc2d  bcd2   0      0     bcd2  bd3    0     0      |
|abc2  b2c2  -bc3   -bc2d abcd  b2cd   -bc2d  -bcd2 abd2  b2d2   -bcd2 -bd3   |
|0     0     abc2   b2c2  0     0      abcd   b2cd  0     0      abd2  b2d2   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2 ab2cd-a2bd2 ab4d-a3bcd a2bc2d-ab3d2 abc3d-ab2d3 abc3-a2c2d ab3c2-a3c3 a2c4|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-b2c3 -ac4 -bc3d -c5  -b2c2d -ac3d -bc2d2 -c4d  -b2cd2 -ac2d2 -bcd3 -c3d2 -b2|
|c4    c3d  0     0    c3d    c2d2  0      0     c2d2   cd3    0     0     cd3|
|ac3   bc3  -c4   -c3d ac2d   bc2d  -c3d   -c2d2 acd2   bcd2   -c2d2 -cd3  ad3|
|0     0    ac3   bc3  0      0     ac2d   bc2d  0      0      acd2  bcd2  0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-ab2c2d ac5-abc2d2 abc2d-a2cd2 ab3cd-a3c2d a2c3d-ab2cd2 ac4d-abcd3 abcd2-a2d3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d3 -acd3 -bd4 -c2d3 a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   0|
|   d4    0    0     0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   0|
|   bd3   -cd3 -d4   0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d 0|
|   0     ad3  bd3   0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   a|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| ab3d2-a3cd2 a2c2d2-ab2d3 ac3d2-abd4 b4c-ab3d b6-a2b3c ab3c2-b5d b3c3-b4d2 b3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0 |
|   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0 |
|   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   ac|
|2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2-ab2cd b5c-a2b2c2 ab2c3-b4cd b2c4-b3cd2 b3cd-ab2d2 b5d-a2b2cd ab2c2d-b4d2 b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0  |
|  0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0  |
|d 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc2|
|  acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2c3d-b3d3 b2c3-abc2d b4c2-a2bc3 abc4-b3c2d bc5-b2c2d2 b2c2d-abcd2 b4cd-a2bc2d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0   |
| 0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0   |
| 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2 |
| bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| abc3d-b3cd2 bc4d-b2cd3 b2cd2-abd3 b4d2-a2bcd2 abc2d2-b3d3 bc3d2-b2d4 bc4-ac3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|0   d3 0  0  0  |)                                                           |
|0   0  d3 0  0  |                                                            |
|0   0  0  d3 0  |                                                            |
|cd2 0  0  0  d3 |                                                            |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d b3c3-a2c4 ac5-b2c3d c6-bc3d2 bc3d-ac2d2 b3c2d-a2c3d ac4d-b2c2d2 c5d-bc2d3 b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2d2-acd3 b3cd2-a2c2d2 ac3d2-b2cd3 c4d2-bcd4 bcd3-ad4 b3d3-a2cd3 ac2d3-b2d4 c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3d3-bd5 a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3 b2c b2d bc2 bcd bd2 c3 c2d |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|---------+-------------------------------------------------------------------|
|         |subquotient ({5} | a b c d a2 ab ac ad b2 bc bd c2 cd d2 |, {5} | a|
|         |                                                                   |
|         |{-1, 4}                                                            |
|         |                                                                   |
|         |                                                                   |
|         |                                                                   |
|---------+-------------------------------------------------------------------|
|         |subquotient ({4} | a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 a2d  abd  acd  a|
|         |             {4} | 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 -a2c -abc -ac2 -|
|         |             {4} | 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 -a2b -ab2 -abc -|
|         |             {4} | 0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d a3   a2b  a2c  a|
|         |                                                                   |
|         |{-1, 3}                                                            |
|---------+-------------------------------------------------------------------|
|cd2 d3 |)|subquotient ({2} | a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 -a2b2 -a3c -a2bd|
|         |             {3} | 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 a2c   a2d  0    |
|         |             {3} | 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 a3    a2b  -a2c |
|         |             {3} | 0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0     0    a3   |
|         |                                                                   |
|         |{-1, 2}                                                            |
|---------+-------------------------------------------------------------------|
|         |subquotient (| a b c d a2bc-a3d a2b3-a4c a3c2-a2b2d a2c3-a2bd2 ab2c|
|         |                                                                   |
|         |{-1, 1}                                                            |
|         |                                                                   |
|         |                                                                   |
|         |                                                                   |
|---------+-------------------------------------------------------------------|
|         |0                                                                  |
|         |                                                                   |
|         |{-1, 0}                                                            |
|---------+-------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2 ab ac ad b2 bc bd c2 cd d2 |)                                              |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2  b2d  bcd  bd2  c2d  cd2  d3   a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0|
|acd -b2c -bc2 -bcd -c3  -c2d -cd2 0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0|
|abd -b3  -b2c -b2d -bc2 -bcd -bd2 0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  a|
|2d  ab2  abc  abd  ac2  acd  ad2  0  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| -a2c2 -ab3 -a2bc -ab2d -abc2 -ab2c -a2c2 -abcd -ac3 -ab2d -a2cd -abd2 -ac2d |
| 0     abc  abd   0     0     ac2   acd   0     0    acd   ad2   0     0     |
| -a2d  a2b  ab2   -abc  -abd  a2c   abc   -ac2  -acd a2d   abd   -acd  -ad2  |
| a2b   0    0     a2b   ab2   0     0     a2c   abc  0     0     a2d   abd   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-a2bd ab4-a3bc a2bc2-ab3d abc3-ab2d2 abc2-a2cd ab3c-a3c2 a2c3-ab2cd ac4-abcd2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |
|  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |
|d 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |
|  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-b4 -ab2c -b3d -b2c2 -b3c -abc2 -b2cd -bc3 -b3d -abcd -b2d2 -bc2d -b2c2 -ac3 |
|b2c b2d   0    0     bc2  bcd   0     0    bcd  bd2   0     0     c3    c2d  |
|ab2 b3    -b2c -b2d  abc  b2c   -bc2  -bcd abd  b2d   -bcd  -bd2  ac2   bc2  |
|0   0     ab2  b3    0    0     abc   b2c  0    0     abd   b2d   0     0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| abcd-a2d2 ab3d-a3cd a2c2d-ab2d2 ac3d-abd3 b3c-ab2d b5-a2b2c ab2c2-b4d b2c3-b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
||, {4} | a2d  abd  acd  ad2  b2d  bcd  bd2  c2d  cd2  d3   a2 0  0  0  ab 0  |
||  {4} | -a2c -abc -ac2 -acd -b2c -bc2 -bcd -c3  -c2d -cd2 0  a2 0  0  0  ab |
||  {4} | -a2b -ab2 -abc -abd -b3  -b2c -b2d -bc2 -bcd -bd2 0  0  a2 0  0  0  |
||  {4} | a3   a2b  a2c  a2d  ab2  abc  abd  ac2  acd  ad2  0  0  0  a2 0  0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-bc2d -c4  -b2cd -ac2d -bcd2 -c3d -b2d2 -acd2 -bd3 -c2d2 a2 0  0  0  ab 0  0 |
|0     0    c2d   cd2   0     0    cd2   d3    0    0     0  a2 0  0  0  ab 0 |
|-c3   -c2d acd   bcd   -c2d  -cd2 ad2   bd2   -cd2 -d3   0  0  a2 0  0  0  ab|
|ac2   bc2  0     0     acd   bcd  0     0     ad2  bd2   0  0  0  a2 0  0  0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3d2 b2c2-abcd b4c-a2bc2 abc3-b3cd bc4-b2cd2 b2cd-abd2 b4d-a2bcd abc2d-b3d2 bc|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0 |
|0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0 |
|ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0 |
|0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  c|
| 0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0|
| 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0|
| ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3d-b2d3 bc3-ac2d b3c2-a2c3 ac4-b2c2d c5-bc2d2 bc2d-acd2 b3cd-a2c2d ac3d-b2cd2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| cd 0  0  0  d2 0  0  0  |)                                                  |
| 0  cd 0  0  0  d2 0  0  |                                                   |
| 0  0  cd 0  0  0  d2 0  |                                                   |
| 0  0  0  cd 0  0  0  d2 |                                                   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d 0  0  0  d2 0  0  0  |, {2} | -a2b2 -a3c -a2bd -a2c2 -ab3 -a2bc -ab2d -abc2|
|  cd 0  0  0  d2 0  0  |  {3} | a2c   a2d  0     0     abc  abd   0     0    |
|  0  cd 0  0  0  d2 0  |  {3} | a3    a2b  -a2c  -a2d  a2b  ab2   -abc  -abd |
|  0  0  cd 0  0  0  d2 |  {3} | 0     0    a3    a2b   0    0     a2b   ab2  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| c4d-bcd3 bcd2-ad3 b3d2-a2cd2 ac2d2-b2d3 c3d2-bd4 a2 ab ac ad b2 bc bd c2 cd |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| -ab2c -a2c2 -abcd -ac3 -ab2d -a2cd -abd2 -ac2d -b4 -ab2c -b3d -b2c2 -b3c -ab|
| ac2   acd   0     0    acd   ad2   0     0     b2c b2d   0    0     bc2  bcd|
| a2c   abc   -ac2  -acd a2d   abd   -acd  -ad2  ab2 b3    -b2c -b2d  abc  b2c|
| 0     0     a2c   abc  0     0     a2d   abd   0   0     ab2  b3    0    0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2 |, | a2bc-a3d a2b3-a4c a3c2-a2b2d a2c3-a2bd2 ab2c-a2bd ab4-a3bc a2bc2-ab3d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2 -b2cd -bc3 -b3d -abcd -b2d2 -bc2d -b2c2 -ac3 -bc2d -c4  -b2cd -ac2d -bcd2 |
|   0     0    bcd  bd2   0     0     c3    c2d  0     0    c2d   cd2   0     |
|   -bc2  -bcd abd  b2d   -bcd  -bd2  ac2   bc2  -c3   -c2d acd   bcd   -c2d  |
|   abc   b2c  0    0     abd   b2d   0     0    ac2   bc2  0     0     acd   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| abc3-ab2d2 abc2-a2cd ab3c-a3c2 a2c3-ab2cd ac4-abcd2 abcd-a2d2 ab3d-a3cd a2c2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-c3d -b2d2 -acd2 -bd3 -c2d2 a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b|
|0    cd2   d3    0    0     0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0|
|-cd2 ad2   bd2   -cd2 -d3   0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0|
|bcd  0     0     ad2  bd2   0  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d-ab2d2 ac3d-abd3 b3c-ab2d b5-a2b2c ab2c2-b4d b2c3-b3d2 b2c2-abcd b4c-a2bc2 a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |)    |
|  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |     |
|  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |     |
|  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |     |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bc3-b3cd bc4-b2cd2 b2cd-abd2 b4d-a2bcd abc2d-b3d2 bc3d-b2d3 bc3-ac2d b3c2-a2c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3 ac4-b2c2d c5-bc2d2 bc2d-acd2 b3cd-a2c2d ac3d-b2cd2 c4d-bcd3 bcd2-ad3 b3d2-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|---------------------------------------------------------+-------------------|
|                                                         |0                  |
|                                                         |                   |
|                                                         |{0, 4}             |
|                                                         |                   |
|                                                         |                   |
|                                                         |                   |
|---------------------------------------------------------+-------------------|
|                                                         |cokernel {5} | a b |
|                                                         |                   |
|                                                         |{0, 3}             |
|                                                         |                   |
|                                                         |                   |
|                                                         |                   |
|---------------------------------------------------------+-------------------|
|                                                         |cokernel {4} | ad  |
|                                                         |         {4} | -ac |
|                                                         |         {4} | -ab |
|                                                         |         {4} | a2  |
|                                                         |                   |
|                                                         |{0, 2}             |
|---------------------------------------------------------+-------------------|
|2cd2 ac2d2-b2d3 c3d2-bd4 a2 ab ac ad b2 bc bd c2 cd d2 |)|cokernel {2} | -ab2|
|                                                         |         {3} | ac  |
|                                                         |         {3} | a2  |
|                                                         |         {3} | 0   |
|                                                         |                   |
|                                                         |{0, 1}             |
|---------------------------------------------------------+-------------------|
|                                                         |cokernel | abc-a2d |
|                                                         |                   |
|                                                         |{0, 0}             |
|---------------------------------------------------------+-------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c d |                                                                        |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bd  cd  d2  a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 |                                |
|-bc -c2 -cd 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 |                                |
|-b2 -bc -bd 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 |                                |
|ab  ac  ad  0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d |                                |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| -a2c -abd -ac2 -b3 -abc -b2d -bc2 -b2c -ac2 -bcd -c3 -b2d -acd -bd2 -c2d a 0|
| ad   0    0    bc  bd   0    0    c2   cd   0    0   cd   d2   0    0    0 a|
| ab   -ac  -ad  ab  b2   -bc  -bd  ac   bc   -c2  -cd ad   bd   -cd  -d2  0 0|
| 0    a2   ab   0   0    ab   b2   0    0    ac   bc  0    0    ad   bd   0 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|ab3-a3c a2c2-ab2d ac3-abd2 b2c-abd b4-a2bc abc2-b3d bc3-b2d2 bc2-acd b3c-a2c2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|--------------------------------------------------------------+              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|--------------------------------------------------------------+              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|--------------------------------------------------------------+              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|--------------------------------------------------------------+              |
| 0 0 b 0 0 0 c 0 0 0 d 0 0 0 |                                |              |
| 0 0 0 b 0 0 0 c 0 0 0 d 0 0 |                                |              |
| a 0 0 0 b 0 0 0 c 0 0 0 d 0 |                                |              |
| 0 a 0 0 0 b 0 0 0 c 0 0 0 d |                                |              |
|                                                              |              |
|                                                              |              |
|--------------------------------------------------------------+              |
| ac3-b2cd c4-bcd2 bcd-ad2 b3d-a2cd ac2d-b2d2 c3d-bd3 a b c d ||              |
|                                                              |              |
|                                                              |              |
|--------------------------------------------------------------+              |
+-----------------------------------------------------------------------------+
|i7 : E^1                                                                     |
|                                                                             |
|     +-----------------------------------------------------------------------|
|o7 = |subquotient (| a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab|
|     |                                                                       |
|     |{-4, 4}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 3}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 2}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 1}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 0}                                                                |
|     +-----------------------------------------------------------------------|
|                                                                             |
|o7 : SpectralSequencePage                                                    |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d3 c4 c3d c2d2 cd3 d4 a4bc-a5d a4b3-a6c a5c2-a4b2d a4c3-a4bd2 a3b2c-a4bd a3b4|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-a5bc a4bc2-a3b3d a3bc3-a3b2d2 a3bc2-a4cd a3b3c-a5c2 a4c3-a3b2cd a3c4-a3bcd2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|a3bcd-a4d2 a3b3d-a5cd a4c2d-a3b2d2 a3c3d-a3bd3 a2b3c-a3b2d a2b5-a4b2c a3b2c2-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|a2b4d a2b2c3-a2b3d2 a2b2c2-a3bcd a2b4c-a4bc2 a3bc3-a2b3cd a2bc4-a2b2cd2 a2b2c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d-a3bd2 a2b4d-a4bcd a3bc2d-a2b3d2 a2bc3d-a2b2d3 a2bc3-a3c2d a2b3c2-a4c3 a3c4-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|a2b2c2d a2c5-a2bc2d2 a2bc2d-a3cd2 a2b3cd-a4c2d a3c3d-a2b2cd2 a2c4d-a2bcd3 a2b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|cd2-a3d3 a2b3d2-a4cd2 a3c2d2-a2b2d3 a2c3d2-a2bd4 ab4c-a2b3d ab6-a3b3c a2b3c2-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|ab5d ab3c3-ab4d2 ab3c2-a2b2cd ab5c-a3b2c2 a2b2c3-ab4cd ab2c4-ab3cd2 ab3cd-a2b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2d2 ab5d-a3b2cd a2b2c2d-ab4d2 ab2c3d-ab3d3 ab2c3-a2bc2d ab4c2-a3bc3 a2bc4-ab3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c2d abc5-ab2c2d2 ab2c2d-a2bcd2 ab4cd-a3bc2d a2bc3d-ab3cd2 abc4d-ab2cd3 ab2cd2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-a2bd3 ab4d2-a3bcd2 a2bc2d2-ab3d3 abc3d2-ab2d4 abc4-a2c3d ab3c3-a3c4 a2c5-ab2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c3d ac6-abc3d2 abc3d-a2c2d2 ab3c2d-a3c3d a2c4d-ab2c2d2 ac5d-abc2d3 abc2d2-a2c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d3 ab3cd2-a3c2d2 a2c3d2-ab2cd3 ac4d2-abcd4 abcd3-a2d4 ab3d3-a3cd3 a2c2d3-ab2d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|4 ac3d3-abd5 b5c-ab4d b7-a2b4c ab4c2-b6d b4c3-b5d2 b4c2-ab3cd b6c-a2b3c2 ab3c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|3-b5cd b3c4-b4cd2 b4cd-ab3d2 b6d-a2b3cd ab3c2d-b5d2 b3c3d-b4d3 b3c3-ab2c2d b5|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c2-a2b2c3 ab2c4-b4c2d b2c5-b3c2d2 b3c2d-ab2cd2 b5cd-a2b2c2d ab2c3d-b4cd2 b2c4|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d-b3cd3 b3cd2-ab2d3 b5d2-a2b2cd2 ab2c2d2-b4d3 b2c3d2-b3d4 b2c4-abc3d b4c3-a2b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c4 abc5-b3c3d bc6-b2c3d2 b2c3d-abc2d2 b4c2d-a2bc3d abc4d-b3c2d2 bc5d-b2c2d3 b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2c2d2-abcd3 b4cd2-a2bc2d2 abc3d2-b3cd3 bc4d2-b2cd4 b2cd3-abd4 b4d3-a2bcd3 abc|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2d3-b3d4 bc3d3-b2d5 bc5-ac4d b3c4-a2c5 ac6-b2c4d c7-bc4d2 bc4d-ac3d2 b3c3d-a2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c4d ac5d-b2c3d2 c6d-bc3d3 bc3d2-ac2d3 b3c2d2-a2c3d2 ac4d2-b2c2d3 c5d2-bc2d4 b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c2d3-acd4 b3cd3-a2c2d3 ac3d3-b2cd4 c4d3-bcd5 bcd4-ad5 b3d4-a2cd4 ac2d4-b2d5 c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|3d4-bd6 0 |, | a4bc-a5d a4b3-a6c a5c2-a4b2d a4c3-a4bd2 a3b2c-a4bd a3b4-a5bc a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|4bc2-a3b3d a3bc3-a3b2d2 a3bc2-a4cd a3b3c-a5c2 a4c3-a3b2cd a3c4-a3bcd2 a3bcd-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|4d2 a3b3d-a5cd a4c2d-a3b2d2 a3c3d-a3bd3 a2b3c-a3b2d a2b5-a4b2c a3b2c2-a2b4d a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2b2c3-a2b3d2 a2b2c2-a3bcd a2b4c-a4bc2 a3bc3-a2b3cd a2bc4-a2b2cd2 a2b2cd-a3bd2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| a2b4d-a4bcd a3bc2d-a2b3d2 a2bc3d-a2b2d3 a2bc3-a3c2d a2b3c2-a4c3 a3c4-a2b2c2d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| a2c5-a2bc2d2 a2bc2d-a3cd2 a2b3cd-a4c2d a3c3d-a2b2cd2 a2c4d-a2bcd3 a2bcd2-a3d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|3 a2b3d2-a4cd2 a3c2d2-a2b2d3 a2c3d2-a2bd4 ab4c-a2b3d ab6-a3b3c a2b3c2-ab5d ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|3c3-ab4d2 ab3c2-a2b2cd ab5c-a3b2c2 a2b2c3-ab4cd ab2c4-ab3cd2 ab3cd-a2b2d2 ab5|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d-a3b2cd a2b2c2d-ab4d2 ab2c3d-ab3d3 ab2c3-a2bc2d ab4c2-a3bc3 a2bc4-ab3c2d abc|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|5-ab2c2d2 ab2c2d-a2bcd2 ab4cd-a3bc2d a2bc3d-ab3cd2 abc4d-ab2cd3 ab2cd2-a2bd3 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|ab4d2-a3bcd2 a2bc2d2-ab3d3 abc3d2-ab2d4 abc4-a2c3d ab3c3-a3c4 a2c5-ab2c3d ac6|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-abc3d2 abc3d-a2c2d2 ab3c2d-a3c3d a2c4d-ab2c2d2 ac5d-abc2d3 abc2d2-a2cd3 ab3c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d2-a3c2d2 a2c3d2-ab2cd3 ac4d2-abcd4 abcd3-a2d4 ab3d3-a3cd3 a2c2d3-ab2d4 ac3d3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-abd5 b5c-ab4d b7-a2b4c ab4c2-b6d b4c3-b5d2 b4c2-ab3cd b6c-a2b3c2 ab3c3-b5cd |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|b3c4-b4cd2 b4cd-ab3d2 b6d-a2b3cd ab3c2d-b5d2 b3c3d-b4d3 b3c3-ab2c2d b5c2-a2b2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c3 ab2c4-b4c2d b2c5-b3c2d2 b3c2d-ab2cd2 b5cd-a2b2c2d ab2c3d-b4cd2 b2c4d-b3cd3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| b3cd2-ab2d3 b5d2-a2b2cd2 ab2c2d2-b4d3 b2c3d2-b3d4 b2c4-abc3d b4c3-a2bc4 abc5|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-b3c3d bc6-b2c3d2 b2c3d-abc2d2 b4c2d-a2bc3d abc4d-b3c2d2 bc5d-b2c2d3 b2c2d2-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|bcd3 b4cd2-a2bc2d2 abc3d2-b3cd3 bc4d2-b2cd4 b2cd3-abd4 b4d3-a2bcd3 abc2d3-b3d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|4 bc3d3-b2d5 bc5-ac4d b3c4-a2c5 ac6-b2c4d c7-bc4d2 bc4d-ac3d2 b3c3d-a2c4d ac5|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d-b2c3d2 c6d-bc3d3 bc3d2-ac2d3 b3c2d2-a2c3d2 ac4d2-b2c2d3 c5d2-bc2d4 bc2d3-ac|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d4 b3cd3-a2c2d3 ac3d3-b2cd4 c4d3-bcd5 bcd4-ad5 b3d4-a2cd4 ac2d4-b2d5 c3d4-bd6|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----+-----------------------------------------------------------------------|
| 0 |)|subquotient ({2} | a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   |
|     |             {3} | 0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d |
|     |             {3} | 0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   |
|     |             {3} | 0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   |
|     |                                                                       |
|     |{-3, 4}                                                                |
|-----+-----------------------------------------------------------------------|
|     |subquotient (| a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3 b2c b2d bc2 bc|
|     |                                                                       |
|     |{-3, 3}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|-----+-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-3, 2}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|-----+-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-3, 1}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|-----+-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-3, 0}                                                                |
|-----+-----------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0|
|0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   a|
|a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0|
|0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d bd2 c3 c2d cd2 d3 a3bc-a4d a3b3-a5c a4c2-a3b2d a3c3-a3bd2 a2b2c-a3bd a2b4-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0 |
|cd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc|
|   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0 |
|   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|4bc a3bc2-a2b3d a2bc3-a2b2d2 a2bc2-a3cd a2b3c-a4c2 a3c3-a2b2cd a2c4-a2bcd2 a2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  0   0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0  |
|2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2|
|  bc2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0  |
|  0   bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bcd-a3d2 a2b3d-a4cd a3c2d-a2b2d2 a2c3d-a2bd3 ab3c-a2b2d ab5-a3b2c a2b2c2-ab4d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   0   d3 0  0  0  -a3b2 -a4c -a3bd -a3c2 -a2b3 -a3bc -a2b2d -a2bc2 -a2b2c |
| 0   0   0  d3 0  0  a3c   a3d  0     0     a2bc  a2bd  0      0      a2c2   |
| cd2 0   0  0  d3 0  a4    a3b  -a3c  -a3d  a3b   a2b2  -a2bc  -a2bd  a3c    |
| 0   cd2 0  0  0  d3 0     0    a4    a3b   0     0     a3b    a2b2   0      |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| ab2c3-ab3d2 ab2c2-a2bcd ab4c-a3bc2 a2bc3-ab3cd abc4-ab2cd2 ab2cd-a2bd2 ab4d-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-a3c2 -a2bcd -a2c3 -a2b2d -a3cd -a2bd2 -a2c2d -ab4 -a2b2c -ab3d -ab2c2 -ab3c |
|a2cd  0      0     a2cd   a2d2  0      0      ab2c ab2d   0     0      abc2  |
|a2bc  -a2c2  -a2cd a3d    a2bd  -a2cd  -a2d2  a2b2 ab3    -ab2c -ab2d  a2bc  |
|0     a3c    a2bc  0      0     a3d    a2bd   0    0      a2b2  ab3    0     |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a3bcd a2bc2d-ab3d2 abc3d-ab2d3 abc3-a2c2d ab3c2-a3c3 a2c4-ab2c2d ac5-abc2d2 a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-a2bc2 -ab2cd -abc3 -ab3d -a2bcd -ab2d2 -abc2d -ab2c2 -a2c3 -abc2d -ac4  -ab2|
|abcd   0      0     abcd  abd2   0      0      ac3    ac2d  0      0     ac2d|
|ab2c   -abc2  -abcd a2bd  ab2d   -abcd  -abd2  a2c2   abc2  -ac3   -ac2d a2cd|
|0      a2bc   ab2c  0     0      a2bd   ab2d   0      0     a2c2   abc2  0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bc2d-a2cd2 ab3cd-a3c2d a2c3d-ab2cd2 ac4d-abcd3 abcd2-a2d3 ab3d2-a3cd2 a2c2d2-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|cd -a2c2d -abcd2 -ac3d -ab2d2 -a2cd2 -abd3 -ac2d2 -b5 -ab3c -b4d -b3c2 -b4c -|
|   acd2   0      0     acd2   ad3    0     0      b3c b3d   0    0     b2c2 b|
|   abcd   -ac2d  -acd2 a2d2   abd2   -acd2 -ad3   ab3 b4    -b3c -b3d  ab2c b|
|   0      a2cd   abcd  0      0      a2d2  abd2   0   0     ab3  b4    0    0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|ab2d3 ac3d2-abd4 b4c-ab3d b6-a2b3c ab3c2-b5d b3c3-b4d2 b3c2-ab2cd b5c-a2b2c2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|ab2c2 -b3cd -b2c3 -b4d -ab2cd -b3d2 -b2c2d -b3c2 -abc3 -b2c2d -bc4  -b3cd -ab|
|2cd   0     0     b2cd b2d2   0     0      bc3   bc2d  0      0     bc2d  bcd|
|3c    -b2c2 -b2cd ab2d b3d    -b2cd -b2d2  abc2  b2c2  -bc3   -bc2d abcd  b2c|
|      ab2c  b3c   0    0      ab2d  b3d    0     0     abc2   b2c2  0     0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|ab2c3-b4cd b2c4-b3cd2 b3cd-ab2d2 b5d-a2b2cd ab2c2d-b4d2 b2c3d-b3d3 b2c3-abc2d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c2d -b2cd2 -bc3d -b3d2 -abcd2 -b2d3 -bc2d2 -b2c3 -ac4 -bc3d -c5  -b2c2d -ac3d|
|2   0      0     bcd2  bd3    0     0      c4    c3d  0     0    c3d    c2d2 |
|d   -bc2d  -bcd2 abd2  b2d2   -bcd2 -bd3   ac3   bc3  -c4   -c3d ac2d   bc2d |
|    abcd   b2cd  0     0      abd2  b2d2   0     0    ac3   bc3  0      0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| b4c2-a2bc3 abc4-b3c2d bc5-b2c2d2 b2c2d-abcd2 b4cd-a2bc2d abc3d-b3cd2 bc4d-b2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| -bc2d2 -c4d  -b2cd2 -ac2d2 -bcd3 -c3d2 -b2d3 -acd3 -bd4 -c2d3 a4 0  0  0  a3|
| 0      0     c2d2   cd3    0     0     cd3   d4    0    0     0  a4 0  0  0 |
| -c3d   -c2d2 acd2   bcd2   -c2d2 -cd3  ad3   bd3   -cd3 -d4   0  0  a4 0  0 |
| ac2d   bc2d  0      0      acd2  bcd2  0     0     ad3  bd3   0  0  0  a4 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|cd3 b2cd2-abd3 b4d2-a2bcd2 abc2d2-b3d3 bc3d2-b2d4 bc4-ac3d b3c3-a2c4 ac5-b2c3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|b 0   0   0   a3c 0   0   0   a3d 0   0   0   a2b2 0    0    0    a2bc 0    0|
|  a3b 0   0   0   a3c 0   0   0   a3d 0   0   0    a2b2 0    0    0    a2bc 0|
|  0   a3b 0   0   0   a3c 0   0   0   a3d 0   0    0    a2b2 0    0    0    a|
|  0   0   a3b 0   0   0   a3c 0   0   0   a3d 0    0    0    a2b2 0    0    0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d c6-bc3d2 bc3d-ac2d2 b3c2d-a2c3d ac4d-b2c2d2 c5d-bc2d3 bc2d2-acd3 b3cd2-a2c2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0  |
|    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d|
|2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0  |
|    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2 ac3d2-b2cd3 c4d2-bcd4 bcd3-ad4 b3d3-a2cd3 ac2d3-b2d4 c3d3-bd5 a4 a3b a3c a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  0    0    ab3 0   0   0   ab2c 0    0    0    ab2d 0    0    0    abc2 0   |
|2 0    0    0   ab3 0   0   0    ab2c 0    0    0    ab2d 0    0    0    abc2|
|  a2d2 0    0   0   ab3 0   0    0    ab2c 0    0    0    ab2d 0    0    0   |
|  0    a2d2 0   0   0   ab3 0    0    0    ab2c 0    0    0    ab2d 0    0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab2d abc2 abcd abd2 ac3 ac2d acd2 a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0    0    abcd 0    0    0    abd2 0    0    0    ac3 0   0   0   ac2d 0    |
| 0    0    0    abcd 0    0    0    abd2 0    0    0   ac3 0   0   0    ac2d |
| abc2 0    0    0    abcd 0    0    0    abd2 0    0   0   ac3 0   0    0    |
| 0    abc2 0    0    0    abcd 0    0    0    abd2 0   0   0   ac3 0    0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 bd3 c4 c3d c2d2 cd3 d4 |, | a3bc-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0    0    acd2 0    0    0    ad3 0   0   0   b4 0  0  0  b3c 0   0   0   b3d|
|0    0    0    acd2 0    0    0   ad3 0   0   0  b4 0  0  0   b3c 0   0   0  |
|ac2d 0    0    0    acd2 0    0   0   ad3 0   0  0  b4 0  0   0   b3c 0   0  |
|0    ac2d 0    0    0    acd2 0   0   0   ad3 0  0  0  b4 0   0   0   b3c 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|4d a3b3-a5c a4c2-a3b2d a3c3-a3bd2 a2b2c-a3bd a2b4-a4bc a3bc2-a2b3d a2bc3-a2b2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   0   0   b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0    bc3 |
| b3d 0   0   0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0   |
| 0   b3d 0   0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0   |
| 0   0   b3d 0    0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2 a2bc2-a3cd a2b3c-a4c2 a3c3-a2b2cd a2c4-a2bcd2 a2bcd-a3d2 a2b3d-a4cd a3c2d-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0   0   0   bc2d 0    0    0    bcd2 0    0    0    bd3 0   0   0   c4 0  0  |
|bc3 0   0   0    bc2d 0    0    0    bcd2 0    0    0   bd3 0   0   0  c4 0  |
|0   bc3 0   0    0    bc2d 0    0    0    bcd2 0    0   0   bd3 0   0  0  c4 |
|0   0   bc3 0    0    0    bc2d 0    0    0    bcd2 0   0   0   bd3 0  0  0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a2b2d2 a2c3d-a2bd3 ab3c-a2b2d ab5-a3b2c a2b2c2-ab4d ab2c3-ab3d2 ab2c2-a2bcd a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0  c3d 0   0   0   c2d2 0    0    0    cd3 0   0   0   d4 0  0  0  |, {2} | -|
|0  0   c3d 0   0   0    c2d2 0    0    0   cd3 0   0   0  d4 0  0  |  {3} | a|
|0  0   0   c3d 0   0    0    c2d2 0    0   0   cd3 0   0  0  d4 0  |  {3} | a|
|c4 0   0   0   c3d 0    0    0    c2d2 0   0   0   cd3 0  0  0  d4 |  {3} | 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b4c-a3bc2 a2bc3-ab3cd abc4-ab2cd2 ab2cd-a2bd2 ab4d-a3bcd a2bc2d-ab3d2 abc3d-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|a3b2 -a4c -a3bd -a3c2 -a2b3 -a3bc -a2b2d -a2bc2 -a2b2c -a3c2 -a2bcd -a2c3 -a2|
|3c   a3d  0     0     a2bc  a2bd  0      0      a2c2   a2cd  0      0     a2c|
|4    a3b  -a3c  -a3d  a3b   a2b2  -a2bc  -a2bd  a3c    a2bc  -a2c2  -a2cd a3d|
|     0    a4    a3b   0     0     a3b    a2b2   0      0     a3c    a2bc  0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b2d3 abc3-a2c2d ab3c2-a3c3 a2c4-ab2c2d ac5-abc2d2 abc2d-a2cd2 ab3cd-a3c2d a2c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|b2d -a3cd -a2bd2 -a2c2d -ab4 -a2b2c -ab3d -ab2c2 -ab3c -a2bc2 -ab2cd -abc3 -a|
|d   a2d2  0      0      ab2c ab2d   0     0      abc2  abcd   0      0     ab|
|    a2bd  -a2cd  -a2d2  a2b2 ab3    -ab2c -ab2d  a2bc  ab2c   -abc2  -abcd a2|
|    0     a3d    a2bd   0    0      a2b2  ab3    0     0      a2bc   ab2c  0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3d-ab2cd2 ac4d-abcd3 abcd2-a2d3 ab3d2-a3cd2 a2c2d2-ab2d3 ac3d2-abd4 b4c-ab3d |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|b3d -a2bcd -ab2d2 -abc2d -ab2c2 -a2c3 -abc2d -ac4  -ab2cd -a2c2d -abcd2 -ac3d|
|cd  abd2   0      0      ac3    ac2d  0      0     ac2d   acd2   0      0    |
|bd  ab2d   -abcd  -abd2  a2c2   abc2  -ac3   -ac2d a2cd   abcd   -ac2d  -acd2|
|    0      a2bd   ab2d   0      0     a2c2   abc2  0      0      a2cd   abcd |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b6-a2b3c ab3c2-b5d b3c3-b4d2 b3c2-ab2cd b5c-a2b2c2 ab2c3-b4cd b2c4-b3cd2 b3cd|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| -ab2d2 -a2cd2 -abd3 -ac2d2 -b5 -ab3c -b4d -b3c2 -b4c -ab2c2 -b3cd -b2c3 -b4d|
| acd2   ad3    0     0      b3c b3d   0    0     b2c2 b2cd   0     0     b2cd|
| a2d2   abd2   -acd2 -ad3   ab3 b4    -b3c -b3d  ab2c b3c    -b2c2 -b2cd ab2d|
| 0      0      a2d2  abd2   0   0     ab3  b4    0    0      ab2c  b3c   0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-ab2d2 b5d-a2b2cd ab2c2d-b4d2 b2c3d-b3d3 b2c3-abc2d b4c2-a2bc3 abc4-b3c2d bc5|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| -ab2cd -b3d2 -b2c2d -b3c2 -abc3 -b2c2d -bc4  -b3cd -abc2d -b2cd2 -bc3d -b3d2|
| b2d2   0     0      bc3   bc2d  0      0     bc2d  bcd2   0      0     bcd2 |
| b3d    -b2cd -b2d2  abc2  b2c2  -bc3   -bc2d abcd  b2cd   -bc2d  -bcd2 abd2 |
| 0      ab2d  b3d    0     0     abc2   b2c2  0     0      abcd   b2cd  0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-b2c2d2 b2c2d-abcd2 b4cd-a2bc2d abc3d-b3cd2 bc4d-b2cd3 b2cd2-abd3 b4d2-a2bcd2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| -abcd2 -b2d3 -bc2d2 -b2c3 -ac4 -bc3d -c5  -b2c2d -ac3d -bc2d2 -c4d  -b2cd2 -|
| bd3    0     0      c4    c3d  0     0    c3d    c2d2  0      0     c2d2   c|
| b2d2   -bcd2 -bd3   ac3   bc3  -c4   -c3d ac2d   bc2d  -c3d   -c2d2 acd2   b|
| 0      abd2  b2d2   0     0    ac3   bc3  0      0     ac2d   bc2d  0      0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| abc2d2-b3d3 bc3d2-b2d4 bc4-ac3d b3c3-a2c4 ac5-b2c3d c6-bc3d2 bc3d-ac2d2 b3c2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|ac2d2 -bcd3 -c3d2 -b2d3 -acd3 -bd4 -c2d3 a4 0  0  0  a3b 0   0   0   a3c 0   |
|d3    0     0     cd3   d4    0    0     0  a4 0  0  0   a3b 0   0   0   a3c |
|cd2   -c2d2 -cd3  ad3   bd3   -cd3 -d4   0  0  a4 0  0   0   a3b 0   0   0   |
|      acd2  bcd2  0     0     ad3  bd3   0  0  0  a4 0   0   0   a3b 0   0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d-a2c3d ac4d-b2c2d2 c5d-bc2d3 bc2d2-acd3 b3cd2-a2c2d2 ac3d2-b2cd3 c4d2-bcd4 b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0   0   a3d 0   0   0   a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0  |
|0   0   0   a3d 0   0   0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0  |
|a3c 0   0   0   a3d 0   0    0    a2b2 0    0    0    a2bc 0    0    0    a2b|
|0   a3c 0   0   0   a3d 0    0    0    a2b2 0    0    0    a2bc 0    0    0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|cd3-ad4 b3d3-a2cd3 ac2d3-b2d4 c3d3-bd5 a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0    0    ab3 0   0 |
|  0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0    0   ab3 0 |
|d 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0   0   ab|
|  a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0   0   0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d a2d2 ab3 ab2c ab2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  0   ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0|
|  0   0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0|
|3 0   0    0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    a|
|  ab3 0    0    0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2 bc3 bc2d bcd2 bd3 c4 c3d c2d2 cd3 d4 |)                                   |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|    0    abd2 0    0    0    ac3 0   0   0   ac2d 0    0    0    acd2 0    0 |
|    0    0    abd2 0    0    0   ac3 0   0   0    ac2d 0    0    0    acd2 0 |
|bcd 0    0    0    abd2 0    0   0   ac3 0   0    0    ac2d 0    0    0    ac|
|    abcd 0    0    0    abd2 0   0   0   ac3 0    0    0    ac2d 0    0    0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|   0    ad3 0   0   0   b4 0  0  0  b3c 0   0   0   b3d 0   0   0   b2c2 0   |
|   0    0   ad3 0   0   0  b4 0  0  0   b3c 0   0   0   b3d 0   0   0    b2c2|
|d2 0    0   0   ad3 0   0  0  b4 0  0   0   b3c 0   0   0   b3d 0   0    0   |
|   acd2 0   0   0   ad3 0  0  0  b4 0   0   0   b3c 0   0   0   b3d 0    0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0    0    b2cd 0    0    0    b2d2 0    0    0    bc3 0   0   0   bc2d 0    |
| 0    0    0    b2cd 0    0    0    b2d2 0    0    0   bc3 0   0   0    bc2d |
| b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0   0   bc3 0   0    0    |
| 0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0   0   0   bc3 0    0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0    0    bcd2 0    0    0    bd3 0   0   0   c4 0  0  0  c3d 0   0   0   c2d|
|0    0    0    bcd2 0    0    0   bd3 0   0   0  c4 0  0  0   c3d 0   0   0  |
|bc2d 0    0    0    bcd2 0    0   0   bd3 0   0  0  c4 0  0   0   c3d 0   0  |
|0    bc2d 0    0    0    bcd2 0   0   0   bd3 0  0  0  c4 0   0   0   c3d 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------+-----------------------------|
|2 0    0    0    cd3 0   0   0   d4 0  0  0  |)|subquotient ({4} | a2 0  0  0|
|  c2d2 0    0    0   cd3 0   0   0  d4 0  0  | |             {4} | 0  a2 0  0|
|  0    c2d2 0    0   0   cd3 0   0  0  d4 0  | |             {4} | 0  0  a2 0|
|  0    0    c2d2 0   0   0   cd3 0  0  0  d4 | |             {4} | 0  0  0  a|
|                                               |                             |
|                                               |{-2, 4}                      |
|-----------------------------------------------+-----------------------------|
|                                               |subquotient ({2} | a2 0  0  0|
|                                               |             {3} | 0  a2 0  0|
|                                               |             {3} | 0  0  a2 0|
|                                               |             {3} | 0  0  0  a|
|                                               |                             |
|                                               |{-2, 3}                      |
|-----------------------------------------------+-----------------------------|
|                                               |subquotient (| a2 ab ac ad b2|
|                                               |                             |
|                                               |{-2, 2}                      |
|                                               |                             |
|                                               |                             |
|                                               |                             |
|-----------------------------------------------+-----------------------------|
|                                               |0                            |
|                                               |                             |
|                                               |{-2, 1}                      |
|                                               |                             |
|                                               |                             |
|                                               |                             |
|-----------------------------------------------+-----------------------------|
|                                               |0                            |
|                                               |                             |
|                                               |{-2, 0}                      |
|-----------------------------------------------+-----------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 |
|  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  |
|  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  |
|2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 |
|  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  |
|  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  |
|2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| bc bd c2 cd d2 a2bc-a3d a2b3-a4c a3c2-a2b2d a2c3-a2bd2 ab2c-a2bd ab4-a3bc a2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0  0  0  cd 0  0  0  d2 0  0  0  a2d  abd  acd  ad2  b2d  bcd  bd2  c2d  cd2 |
|c2 0  0  0  cd 0  0  0  d2 0  0  -a2c -abc -ac2 -acd -b2c -bc2 -bcd -c3  -c2d|
|0  c2 0  0  0  cd 0  0  0  d2 0  -a2b -ab2 -abc -abd -b3  -b2c -b2d -bc2 -bcd|
|0  0  c2 0  0  0  cd 0  0  0  d2 a3   a2b  a2c  a2d  ab2  abc  abd  ac2  acd |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|0  0  0  cd 0  0  0  d2 0  0  0  -a2b2 -a3c -a2bd -a2c2 -ab3 -a2bc -ab2d -abc|
|c2 0  0  0  cd 0  0  0  d2 0  0  a2c   a2d  0     0     abc  abd   0     0   |
|0  c2 0  0  0  cd 0  0  0  d2 0  a3    a2b  -a2c  -a2d  a2b  ab2   -abc  -abd|
|0  0  c2 0  0  0  cd 0  0  0  d2 0     0    a3    a2b   0    0     a2b   ab2 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bc2-ab3d abc3-ab2d2 abc2-a2cd ab3c-a3c2 a2c3-ab2cd ac4-abcd2 abcd-a2d2 ab3d-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| d3   a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0  |
| -cd2 0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0  |
| -bd2 0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2|
| ad2  0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2 -ab2c -a2c2 -abcd -ac3 -ab2d -a2cd -abd2 -ac2d -b4 -ab2c -b3d -b2c2 -b3c -a|
|  ac2   acd   0     0    acd   ad2   0     0     b2c b2d   0    0     bc2  bc|
|  a2c   abc   -ac2  -acd a2d   abd   -acd  -ad2  ab2 b3    -b2c -b2d  abc  b2|
|  0     0     a2c   abc  0     0     a2d   abd   0   0     ab2  b3    0    0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3cd a2c2d-ab2d2 ac3d-abd3 b3c-ab2d b5-a2b2c ab2c2-b4d b2c3-b3d2 b2c2-abcd b4c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   |
| 0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 |
| 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   |
| ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bc2 -b2cd -bc3 -b3d -abcd -b2d2 -bc2d -b2c2 -ac3 -bc2d -c4  -b2cd -ac2d -bcd2|
|d   0     0    bcd  bd2   0     0     c3    c2d  0     0    c2d   cd2   0    |
|c   -bc2  -bcd abd  b2d   -bcd  -bd2  ac2   bc2  -c3   -c2d acd   bcd   -c2d |
|    abc   b2c  0    0     abd   b2d   0     0    ac2   bc2  0     0     acd  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-a2bc2 abc3-b3cd bc4-b2cd2 b2cd-abd2 b4d-a2bcd abc2d-b3d2 bc3d-b2d3 bc3-ac2d |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0|
|0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0|
|ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   b|
|0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| -c3d -b2d2 -acd2 -bd3 -c2d2 a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d |
| 0    cd2   d3    0    0     0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   |
| -cd2 ad2   bd2   -cd2 -d3   0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   |
| bcd  0     0     ad2  bd2   0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b3c2-a2c3 ac4-b2c2d c5-bc2d2 bc2d-acd2 b3cd-a2c2d ac3d-b2cd2 c4d-bcd3 bcd2-ad|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0   0   d3 0  0  0|
|   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0   0   0  d3 0  0|
|cd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2 0   0  0  d3 0|
|   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0   cd2 0  0  0  d|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   a|
|a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0|
|0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0|
|0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3 b3d2-a2cd2 ac2d2-b2d3 c3d2-bd4 a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3 b2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  |, {4} | a2d  abd  acd  ad2  b2d  bcd  bd2  c2d  cd2  d3   a3 0  0  0  a2b |
|  |  {4} | -a2c -abc -ac2 -acd -b2c -bc2 -bcd -c3  -c2d -cd2 0  a3 0  0  0   |
|  |  {4} | -a2b -ab2 -abc -abd -b3  -b2c -b2d -bc2 -bcd -bd2 0  0  a3 0  0   |
|3 |  {4} | a3   a2b  a2c  a2d  ab2  abc  abd  ac2  acd  ad2  0  0  0  a3 0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|cd 0   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc|
|   acd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0 |
|   0   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0 |
|   0   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c b2d bc2 bcd bd2 c3 c2d cd2 d3 |, | a2bc-a3d a2b3-a4c a3c2-a2b2d a2c3-a2bd2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   a|
|a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0|
|0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0|
|0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2 0   0   0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2|
|  bc2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0  |
|  0   bc2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0  |
|  0   0   bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|ab2c-a2bd ab4-a3bc a2bc2-ab3d abc3-ab2d2 abc2-a2cd ab3c-a3c2 a2c3-ab2cd ac4-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|bd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0   b3 0  0  0  b2|
|   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0  b3 0  0  0 |
|   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0  0  b3 0  0 |
|   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0  0  0  b3 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0   0   0   d3 0  0  0  |, {2} | -a2b2 -a3c -a2bd -a2c2 -ab3 -a2bc -ab2d -ab|
| cd2 0   0   0  d3 0  0  |  {3} | a2c   a2d  0     0     abc  abd   0     0  |
| 0   cd2 0   0  0  d3 0  |  {3} | a3    a2b  -a2c  -a2d  a2b  ab2   -abc  -ab|
| 0   0   cd2 0  0  0  d3 |  {3} | 0     0    a3    a2b   0    0     a2b   ab2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bcd2 abcd-a2d2 ab3d-a3cd a2c2d-ab2d2 ac3d-abd3 b3c-ab2d b5-a2b2c ab2c2-b4d b2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0  |
|  b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0  |
|  0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0  |
|  0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2 -ab2c -a2c2 -abcd -ac3 -ab2d -a2cd -abd2 -ac2d -b4 -ab2c -b3d -b2c2 -b3c -|
|   ac2   acd   0     0    acd   ad2   0     0     b2c b2d   0    0     bc2  b|
|d  a2c   abc   -ac2  -acd a2d   abd   -acd  -ad2  ab2 b3    -b2c -b2d  abc  b|
|   0     0     a2c   abc  0     0     a2d   abd   0   0     ab2  b3    0    0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c3-b3d2 b2c2-abcd b4c-a2bc2 abc3-b3cd bc4-b2cd2 b2cd-abd2 b4d-a2bcd abc2d-b3d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| c3 0  0  0  c2d 0   0   0   cd2 0   0   0   d3 0  0  0  |)                  |
| 0  c3 0  0  0   c2d 0   0   0   cd2 0   0   0  d3 0  0  |                   |
| 0  0  c3 0  0   0   c2d 0   0   0   cd2 0   0  0  d3 0  |                   |
| 0  0  0  c3 0   0   0   c2d 0   0   0   cd2 0  0  0  d3 |                   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|abc2 -b2cd -bc3 -b3d -abcd -b2d2 -bc2d -b2c2 -ac3 -bc2d -c4  -b2cd -ac2d -bcd|
|cd   0     0    bcd  bd2   0     0     c3    c2d  0     0    c2d   cd2   0   |
|2c   -bc2  -bcd abd  b2d   -bcd  -bd2  ac2   bc2  -c3   -c2d acd   bcd   -c2d|
|     abc   b2c  0    0     abd   b2d   0     0    ac2   bc2  0     0     acd |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2 bc3d-b2d3 bc3-ac2d b3c2-a2c3 ac4-b2c2d c5-bc2d2 bc2d-acd2 b3cd-a2c2d ac3d-b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2 -c3d -b2d2 -acd2 -bd3 -c2d2 a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d|
|  0    cd2   d3    0    0     0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0  |
|  -cd2 ad2   bd2   -cd2 -d3   0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0  |
|  bcd  0     0     ad2  bd2   0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2cd2 c4d-bcd3 bcd2-ad3 b3d2-a2cd2 ac2d2-b2d3 c3d2-bd4 a3 a2b a2c a2d ab2 abc |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   |
| a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   |
| 0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   |
| 0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|abd ac2 acd ad2 b3 b2c b2d bc2 bcd bd2 c3 c2d cd2 d3 |)                      |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|acd 0   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   b|
|0   acd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0|
|0   0   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0|
|0   0   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2 0   0   0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd|
|   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0 |
|   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0 |
|   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|----------------------------+------------------------------------------------|
|                            |subquotient ({5} | a b c d a2 ab ac ad b2 bc bd |
|                            |                                                |
|                            |{-1, 4}                                         |
|                            |                                                |
|                            |                                                |
|                            |                                                |
|----------------------------+------------------------------------------------|
|2 0   0   0   d3 0  0  0  |)|subquotient ({4} | a 0 0 0 b 0 0 0 c 0 0 0 d 0 0|
|  cd2 0   0   0  d3 0  0  | |             {4} | 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0|
|  0   cd2 0   0  0  d3 0  | |             {4} | 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d|
|  0   0   cd2 0  0  0  d3 | |             {4} | 0 0 0 a 0 0 0 b 0 0 0 c 0 0 0|
|                            |                                                |
|                            |{-1, 3}                                         |
|----------------------------+------------------------------------------------|
|                            |subquotient ({2} | a 0 0 0 b 0 0 0 c 0 0 0 d 0 0|
|                            |             {3} | 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0|
|                            |             {3} | 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d|
|                            |             {3} | 0 0 0 a 0 0 0 b 0 0 0 c 0 0 0|
|                            |                                                |
|                            |{-1, 2}                                         |
|----------------------------+------------------------------------------------|
|                            |subquotient (| a b c d abc-a2d ab3-a3c a2c2-ab2d|
|                            |                                                |
|                            |{-1, 1}                                         |
|                            |                                                |
|                            |                                                |
|                            |                                                |
|----------------------------+------------------------------------------------|
|                            |0                                               |
|                            |                                                |
|                            |{-1, 0}                                         |
|----------------------------+------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c2 cd d2 |, {5} | a2 ab ac ad b2 bc bd c2 cd d2 |)                           |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0 ad  bd  cd  d2  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0|
| 0 -ac -bc -c2 -cd 0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0|
| 0 -ab -b2 -bc -bd 0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0|
| d a2  ab  ac  ad  0  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0 -ab2 -a2c -abd -ac2 -b3 -abc -b2d -bc2 -b2c -ac2 -bcd -c3 -b2d -acd -bd2 -|
| 0 ac   ad   0    0    bc  bd   0    0    c2   cd   0    0   cd   d2   0    0|
| 0 a2   ab   -ac  -ad  ab  b2   -bc  -bd  ac   bc   -c2  -cd ad   bd   -cd  -|
| d 0    0    a2   ab   0   0    ab   b2   0    0    ac   bc  0    0    ad   b|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| ac3-abd2 b2c-abd b4-a2bc abc2-b3d bc3-b2d2 bc2-acd b3c-a2c2 ac3-b2cd c4-bcd2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |, {4} | ad  bd|
|  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |  {4} | -ac -b|
|  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |  {4} | -ab -b|
|2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |  {4} | a2  ab|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2d a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  b|
|    0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0|
|d2  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0|
|d   0  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| bcd-ad2 b3d-a2cd ac2d-b2d2 c3d-bd3 a2 ab ac ad b2 bc bd c2 cd d2 |, | abc-a2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  cd  d2  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0|
|c -c2 -cd 0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0|
|2 -bc -bd 0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  b|
|  ac  ad  0  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |, {2} | -ab2 -a2c -abd -ac2 -|
|  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |  {3} | ac   ad   0    0    b|
|  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |  {3} | a2   ab   -ac  -ad  a|
|  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |  {3} | 0    0    a2   ab   0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d ab3-a3c a2c2-ab2d ac3-abd2 b2c-abd b4-a2bc abc2-b3d bc3-b2d2 bc2-acd b3c-a2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |)                      |
|  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |                       |
|c 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |                       |
|  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |                       |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b3 -abc -b2d -bc2 -b2c -ac2 -bcd -c3 -b2d -acd -bd2 -c2d a2 0  0  0  ab 0  0 |
|c  bd   0    0    c2   cd   0    0   cd   d2   0    0    0  a2 0  0  0  ab 0 |
|b  b2   -bc  -bd  ac   bc   -c2  -cd ad   bd   -cd  -d2  0  0  a2 0  0  0  ab|
|   0    ab   b2   0    0    ac   bc  0    0    ad   bd   0  0  0  a2 0  0  0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2 ac3-b2cd c4-bcd2 bcd-ad2 b3d-a2cd ac2d-b2d2 c3d-bd3 a2 ab ac ad b2 bc bd c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  c|
| 0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0|
| 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0|
| ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2 cd d2 |)                                                                   |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-------------------------+---------------------------------------------------|
|                         |0                                                  |
|                         |                                                   |
|                         |{0, 4}                                             |
|                         |                                                   |
|                         |                                                   |
|                         |                                                   |
|-------------------------+---------------------------------------------------|
|                         |cokernel {5} | a b c d |                           |
|                         |                                                   |
|                         |{0, 3}                                             |
|                         |                                                   |
|                         |                                                   |
|                         |                                                   |
|-------------------------+---------------------------------------------------|
|d 0  0  0  d2 0  0  0  |)|cokernel {4} | d  a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 ||
|  cd 0  0  0  d2 0  0  | |         {4} | -c 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 ||
|  0  cd 0  0  0  d2 0  | |         {4} | -b 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 ||
|  0  0  cd 0  0  0  d2 | |         {4} | a  0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d ||
|                         |                                                   |
|                         |{0, 2}                                             |
|-------------------------+---------------------------------------------------|
|                         |cokernel {2} | -b2 -ac -bd -c2 a 0 0 0 b 0 0 0 c 0 |
|                         |         {3} | c   d   0   0   0 a 0 0 0 b 0 0 0 c |
|                         |         {3} | a   b   -c  -d  0 0 a 0 0 0 b 0 0 0 |
|                         |         {3} | 0   0   a   b   0 0 0 a 0 0 0 b 0 0 |
|                         |                                                   |
|                         |{0, 1}                                             |
|-------------------------+---------------------------------------------------|
|                         |cokernel | bc-ad b3-a2c ac2-b2d c3-bd2 a b c d |   |
|                         |                                                   |
|                         |{0, 0}                                             |
|-------------------------+---------------------------------------------------|
|-----------------------------------------------------------------------------|
|-------------+                                                               |
|             |                                                               |
|             |                                                               |
|             |                                                               |
|             |                                                               |
|             |                                                               |
|             |                                                               |
|-------------+                                                               |
|             |                                                               |
|             |                                                               |
|             |                                                               |
|             |                                                               |
|             |                                                               |
|             |                                                               |
|-------------+                                                               |
|             |                                                               |
|             |                                                               |
|             |                                                               |
|             |                                                               |
|             |                                                               |
|             |                                                               |
|-------------+                                                               |
|0 0 d 0 0 0 ||                                                               |
|0 0 0 d 0 0 ||                                                               |
|c 0 0 0 d 0 ||                                                               |
|0 c 0 0 0 d ||                                                               |
|             |                                                               |
|             |                                                               |
|-------------+                                                               |
|             |                                                               |
|             |                                                               |
|             |                                                               |
|-------------+                                                               |
+-----------------------------------------------------------------------------+
|i8 : E^infinity                                                              |
|                                                                             |
|     +-----------------------------------------------------------------------|
|o8 = |subquotient (| a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab|
|     |                                                                       |
|     |{-4, 4}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 3}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 2}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 1}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 0}                                                                |
|     +-----------------------------------------------------------------------|
|                                                                             |
|o8 : Page                                                                    |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d3 c4 c3d c2d2 cd3 d4 bc-ad b3-a2c ac2-b2d c3-bd2 0 |, | bc-ad b3-a2c ac2-b2d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|------------+----------------------------------------------------------------|
| c3-bd2 0 |)|subquotient ({2} | 0 a2b2 a2bd a2bd 0 a3c  a3c  a2c2 a2b2 ab3  a|
|            |             {3} | 0 -a2c 0    0    0 -a2d -a2d 0    -a2c -abc 0|
|            |             {3} | 0 -a3  a2c  a2c  0 -a2b -a2b a2d  -a3  -a2b a|
|            |             {3} | 0 0    -a3  -a3  0 0    0    -a2b 0    0    -|
|            |                                                                |
|            |{-3, 4}                                                         |
|------------+----------------------------------------------------------------|
|            |subquotient (| a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3 b2c b2d|
|            |                                                                |
|            |{-3, 3}                                                         |
|            |                                                                |
|            |                                                                |
|            |                                                                |
|------------+----------------------------------------------------------------|
|            |0                                                               |
|            |                                                                |
|            |{-3, 2}                                                         |
|            |                                                                |
|            |                                                                |
|            |                                                                |
|------------+----------------------------------------------------------------|
|            |0                                                               |
|            |                                                                |
|            |{-3, 1}                                                         |
|            |                                                                |
|            |                                                                |
|            |                                                                |
|------------+----------------------------------------------------------------|
|            |0                                                               |
|            |                                                                |
|            |{-3, 0}                                                         |
|------------+----------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|b2d ab2d a2bd a2bc a2bc a2bc abc2 abc2 a2c2 ab2c ab2c abcd abcd abcd 0       |
|    0    0    -abd -abd -abd 0    0    0    -ac2 -ac2 0    0    0    acd     |
|bc  abc  a2c  -ab2 -ab2 -ab2 abd  abd  a2d  -a2c -a2c ac2  ac2  ac2  abc+a2d |
|a2b -a2b -a3  0    0    0    -ab2 -ab2 -a2b 0    0    -a2c -a2c -a2c -a2b    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| bc2 bcd bd2 c3 c2d cd2 d3 bc-ad b3-a2c ac2-b2d c3-bd2 a4 a3b a3c a3d a2b2 a2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|abd2 ac3  abd2 0 a2cd a2cd a2cd ac2d ac2d ab3  ab2c b4   b3d  b3d  ab2d 0    |
|0    0    0    0 -ad2 -ad2 -ad2 0    0    -abc -ac2 -b2c 0    0    0    -ac2+|
|acd  acd  acd  0 -abd -abd -abd ad2  ad2  -a2b -a2c -ab2 b2c  b2c  abc  b3-a2|
|-a2d -abc -a2d 0 0    0    0    -abd -abd 0    0    0    -ab2 -ab2 -a2b 0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|    b2c2 b2c2 abc2 b3c  b3c  b2cd b2cd b2cd abcd 0       b2d2 bc3  b2d2 abd2 |
|b2d 0    0    0    -bc2 -bc2 0    0    0    0    bcd     0    0    0    0    |
|c   b2d  b2d  abd  -abc -abc bc2  bc2  bc2  ac2  b2c+abd bcd  bcd  bcd  acd  |
|    -b3  -b3  -ab2 0    0    -abc -abc -abc -a2c -ab2    -abd -b2c -abd -a2d |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 bd3 c4 c3d c2d2 cd3 d4 |, | bc-ad b3-a2c ac2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0       bc2d bc2d bc3  ac3  0       0        bc2d ac2d 0       bcd2 bcd2 c4  |
|bd2     0    0    0    0    c3      0        0    0    c2d     0    0    0   |
|ac2+b2d bd2  bd2  bcd  acd  ac2+b2d c3-bd2   bd2  ad2  bc2+acd c2d  c2d  c2d |
|-a2c    -b2d -b2d -b2c -abc -b3     -ac2+b2d -b2d -abd -abc    -acd -acd -bc2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-b2d c3-bd2 a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab2d abc2 a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| bcd2 0       bd3  c3d  c3d  0 bd3  0 acd2 acd2 acd2 c2d2 c2d2 0 0 0         |
| 0    cd2     0    0    0    0 0    0 -d3  -d3  -d3  0    0    0 0 -a2cd     |
| c2d  bcd+ad2 cd2  cd2  cd2  0 cd2  0 -bd2 -bd2 -bd2 d3   d3   0 0 -a2bc-a3d |
| -acd -abd    -ad2 -bcd -bcd 0 -ad2 0 0    0    0    -bd2 -bd2 0 0 a3b       |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 bd3 c4 c3d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0         0 0 0 0 0 0 0 0 0 0 0 0 0 0          0 0          0          0 0 0 |
|-a2cd     0 0 0 0 0 0 0 0 0 0 0 0 0 -a2c2+ab2d 0 -abcd      -abcd      0 0 0 |
|-a2bc-a3d 0 0 0 0 0 0 0 0 0 0 0 0 0 ab3-a3c    0 -ab2c-a2bd -ab2c-a2bd 0 0 0 |
|a3b       0 0 0 0 0 0 0 0 0 0 0 0 0 0          0 a2b2       a2b2       0 0 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| c2d2 cd3 d4 |)                                                              |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0 0 0 0         0 0 0 0 0 0 0 0 0 0         0          0         0           |
|0 0 0 -ac3+abd2 0 0 0 0 0 0 0 0 0 -abc2+b3d -a2c2+ab2d -ac3+abd2 -ac3+b2cd+ab|
|0 0 0 0         0 0 0 0 0 0 0 0 0 b4-a2bc   ab3-a3c    0         b3c+ab2d    |
|0 0 0 ab3-a3c   0 0 0 0 0 0 0 0 0 0         0          ab3-a3c   -a3c        |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|   0 0 0 0 0 0         0 0 0 0 0 0 0 0 0 0 0 0 0 0 -b2 -ac -bd -c2 a4 0  0  0|
|d2 0 0 0 0 0 -bc3+ac2d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c   d   0   0   0  a4 0  0|
|   0 0 0 0 0 -b3d+a2cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a   b   -c  -d  0  0  a4 0|
|   0 0 0 0 0 b4-a2bc   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0   0   a   b   0  0  0  a|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  a3b 0   0   0   a3c 0   0   0   a3d 0   0   0   a2b2 0    0    0    a2bc 0 |
|  0   a3b 0   0   0   a3c 0   0   0   a3d 0   0   0    a2b2 0    0    0    a2|
|  0   0   a3b 0   0   0   a3c 0   0   0   a3d 0   0    0    a2b2 0    0    0 |
|4 0   0   0   a3b 0   0   0   a3c 0   0   0   a3d 0    0    0    a2b2 0    0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|   0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2|
|bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0   |
|   a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0   |
|   0    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0    0    0    ab3 0   0   0   ab2c 0    0    0    ab2d 0    0    0    abc2 |
| a2d2 0    0    0   ab3 0   0   0    ab2c 0    0    0    ab2d 0    0    0    |
| 0    a2d2 0    0   0   ab3 0   0    0    ab2c 0    0    0    ab2d 0    0    |
| 0    0    a2d2 0   0   0   ab3 0    0    0    ab2c 0    0    0    ab2d 0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0    0    0    abcd 0    0    0    abd2 0    0    0    ac3 0   0   0   ac2d 0|
|abc2 0    0    0    abcd 0    0    0    abd2 0    0    0   ac3 0   0   0    a|
|0    abc2 0    0    0    abcd 0    0    0    abd2 0    0   0   ac3 0   0    0|
|0    0    abc2 0    0    0    abcd 0    0    0    abd2 0   0   0   ac3 0    0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|    0    0    acd2 0    0    0    ad3 0   0   0   b4 0  0  0  b3c 0   0   0  |
|c2d 0    0    0    acd2 0    0    0   ad3 0   0   0  b4 0  0  0   b3c 0   0  |
|    ac2d 0    0    0    acd2 0    0   0   ad3 0   0  0  b4 0  0   0   b3c 0  |
|    0    ac2d 0    0    0    acd2 0   0   0   ad3 0  0  0  b4 0   0   0   b3c|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| b3d 0   0   0   b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0    |
| 0   b3d 0   0   0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    |
| 0   0   b3d 0   0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    |
| 0   0   0   b3d 0    0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|bc3 0   0   0   bc2d 0    0    0    bcd2 0    0    0    bd3 0   0   0   c4 0 |
|0   bc3 0   0   0    bc2d 0    0    0    bcd2 0    0    0   bd3 0   0   0  c4|
|0   0   bc3 0   0    0    bc2d 0    0    0    bcd2 0    0   0   bd3 0   0  0 |
|0   0   0   bc3 0    0    0    bc2d 0    0    0    bcd2 0   0   0   bd3 0  0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0  0  c3d 0   0   0   c2d2 0    0    0    cd3 0   0   0   d4 0  0  0  |, {2}|
| 0  0  0   c3d 0   0   0    c2d2 0    0    0   cd3 0   0   0  d4 0  0  |  {3}|
| c4 0  0   0   c3d 0   0    0    c2d2 0    0   0   cd3 0   0  0  d4 0  |  {3}|
| 0  c4 0   0   0   c3d 0    0    0    c2d2 0   0   0   cd3 0  0  0  d4 |  {3}|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| | -b2 -ac -bd -c2 a4 0  0  0  a3b 0   0   0   a3c 0   0   0   a3d 0   0   0 |
| | c   d   0   0   0  a4 0  0  0   a3b 0   0   0   a3c 0   0   0   a3d 0   0 |
| | a   b   -c  -d  0  0  a4 0  0   0   a3b 0   0   0   a3c 0   0   0   a3d 0 |
| | 0   0   a   b   0  0  0  a4 0   0   0   a3b 0   0   0   a3c 0   0   0   a3|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    |
|  0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    |
|  0    0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    a2c2 |
|d 0    0    0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0    a2cd 0    0    0    a2d2 0    0    0    ab3 0   0   0   ab2c 0    0    0|
|0    0    a2cd 0    0    0    a2d2 0    0    0   ab3 0   0   0    ab2c 0    0|
|0    0    0    a2cd 0    0    0    a2d2 0    0   0   ab3 0   0    0    ab2c 0|
|a2c2 0    0    0    a2cd 0    0    0    a2d2 0   0   0   ab3 0    0    0    a|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0    abd2 0    0  |
|    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0    abd2 0  |
|    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0    abd|
|b2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  0    ac3 0   0   0   ac2d 0    0    0    acd2 0    0    0    ad3 0   0   0 |
|  0    0   ac3 0   0   0    ac2d 0    0    0    acd2 0    0    0   ad3 0   0 |
|2 0    0   0   ac3 0   0    0    ac2d 0    0    0    acd2 0    0   0   ad3 0 |
|  abd2 0   0   0   ac3 0    0    0    ac2d 0    0    0    acd2 0   0   0   ad|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  b4 0  0  0  b3c 0   0   0   b3d 0   0   0   b2c2 0    0    0    b2cd 0    0|
|  0  b4 0  0  0   b3c 0   0   0   b3d 0   0   0    b2c2 0    0    0    b2cd 0|
|  0  0  b4 0  0   0   b3c 0   0   0   b3d 0   0    0    b2c2 0    0    0    b|
|3 0  0  0  b4 0   0   0   b3c 0   0   0   b3d 0    0    0    b2c2 0    0    0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|    0    b2d2 0    0    0    bc3 0   0   0   bc2d 0    0    0    bcd2 0    0 |
|    0    0    b2d2 0    0    0   bc3 0   0   0    bc2d 0    0    0    bcd2 0 |
|2cd 0    0    0    b2d2 0    0   0   bc3 0   0    0    bc2d 0    0    0    bc|
|    b2cd 0    0    0    b2d2 0   0   0   bc3 0    0    0    bc2d 0    0    0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|   0    bd3 0   0   0   c4 0  0  0  c3d 0   0   0   c2d2 0    0    0    cd3 0|
|   0    0   bd3 0   0   0  c4 0  0  0   c3d 0   0   0    c2d2 0    0    0   c|
|d2 0    0   0   bd3 0   0  0  c4 0  0   0   c3d 0   0    0    c2d2 0    0   0|
|   bcd2 0   0   0   bd3 0  0  0  c4 0   0   0   c3d 0    0    0    c2d2 0   0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-------------------------+---------------------------------------------------|
|   0   0   d4 0  0  0  |)|subquotient ({4} | ad  bd  cd  d2  a2d  0 0 -abd 0 |
|d3 0   0   0  d4 0  0  | |             {4} | -ac -bc -c2 -cd -a2c 0 0 abc  0 |
|   cd3 0   0  0  d4 0  | |             {4} | -ab -b2 -bc -bd -a2b 0 0 ab2  0 |
|   0   cd3 0  0  0  d4 | |             {4} | a2  ab  ac  ad  a3   0 0 -a2b 0 |
|                         |                                                   |
|                         |{-2, 4}                                            |
|-------------------------+---------------------------------------------------|
|                         |subquotient ({2} | 0 ab2 abd abd 0 a2c a2c ac2 ab2 |
|                         |             {3} | 0 -ac 0   0   0 -ad -ad 0   -ac |
|                         |             {3} | 0 -a2 ac  ac  0 -ab -ab ad  -a2 |
|                         |             {3} | 0 0   -a2 -a2 0 0   0   -ab 0   |
|                         |                                                   |
|                         |{-2, 3}                                            |
|-------------------------+---------------------------------------------------|
|                         |subquotient (| a2 ab ac ad b2 bc bd c2 cd d2 bc-ad |
|                         |                                                   |
|                         |{-2, 2}                                            |
|                         |                                                   |
|                         |                                                   |
|                         |                                                   |
|-------------------------+---------------------------------------------------|
|                         |0                                                  |
|                         |                                                   |
|                         |{-2, 1}                                            |
|                         |                                                   |
|                         |                                                   |
|                         |                                                   |
|-------------------------+---------------------------------------------------|
|                         |0                                                  |
|                         |                                                   |
|                         |{-2, 0}                                            |
|-------------------------+---------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0 0 0 -acd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -b2d -abd 0 0 0 -bcd 0 0 0 0 0 0|
|0 0 0 ac2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b2c  abc  0 0 0 bc2  0 0 0 0 0 0|
|0 0 0 abc  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b3   ab2  0 0 0 b2c  0 0 0 0 0 0|
|0 0 0 -a2c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -ab2 -a2b 0 0 0 -abc 0 0 0 0 0 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b3  b2d b2d abd abc abc abc bc2 bc2 ac2 b2c b2c bcd bcd bcd 0     bd2 c3  0 b|
|-bc 0   0   0   -bd -bd -bd 0   0   0   -c2 -c2 0   0   0   cd    0   0   0 0|
|-ab bc  bc  ac  -b2 -b2 -b2 bd  bd  ad  -ac -ac c2  c2  c2  bc+ad cd  cd  0 c|
|0   -ab -ab -a2 0   0   0   -b2 -b2 -ab 0   0   -ac -ac -ac -ab   -ad -bc 0 -|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b3-a2c ac2-b2d c3-bd2 a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3 b2c b2d bc2 b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0 0 0 0 0 0 0 0 0 0 0 -c2d -bcd -acd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
| 0 0 0 0 0 0 0 0 0 0 0 c3   bc2  ac2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
| 0 0 0 0 0 0 0 0 0 0 0 bc2  b2c  abc  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
| 0 0 0 0 0 0 0 0 0 0 0 -ac2 -abc -a2c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2 0 acd acd acd c2d c2d 0 0 0        0        0 0 0 0 0 0 0 0 0 0 0 0 0 0   |
|   0 -d2 -d2 -d2 0   0   0 0 -acd     -acd     0 0 0 0 0 0 0 0 0 0 0 0 0 -ac2|
|d  0 -bd -bd -bd d2  d2  0 0 -abc-a2d -abc-a2d 0 0 0 0 0 0 0 0 0 0 0 0 0 b3-a|
|ad 0 0   0   0   -bd -bd 0 0 a2b      a2b      0 0 0 0 0 0 0 0 0 0 0 0 0 0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|cd bd2 c3 c2d cd2 d3 |, | bc-ad b3-a2c ac2-b2d c3-bd2 a3 a2b a2c a2d ab2 abc |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0 0 d  a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0|
| 0 0 -c 0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0|
| 0 0 -b 0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   a|
| 0 0 a  0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|     0 0        0        0 0 0 0 0 0 0       0 0 0 0 0 0 0 0 -b2 -ac -bd -c2 |
|+b2d 0 -bcd     -bcd     0 0 0 0 0 0 -c3+bd2 0 0 0 0 0 0 0 0 c   d   0   0   |
|2c   0 -b2c-abd -b2c-abd 0 0 0 0 0 0 0       0 0 0 0 0 0 0 0 a   b   -c  -d  |
|     0 ab2      ab2      0 0 0 0 0 0 b3-a2c  0 0 0 0 0 0 0 0 0   0   a   b   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|abd ac2 acd ad2 b3 b2c b2d bc2 bcd bd2 c3 c2d cd2 d3 |)                      |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0 |
|   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad|
|b2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0 |
|   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   a|
|0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0|
|0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0|
|0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0  |
|2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd|
|  ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0  |
|  0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0 |
|   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0 |
|   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0 |
|   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0   0   d3 0  0 |
| 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0   0   0  d3 0 |
| bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2 0   0  0  d3|
| 0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0   cd2 0  0  0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0  |
|  0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0  |
|  0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0  |
|2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0  |, {4} | d  a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   a|
| 0  |  {4} | -c 0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0|
| 0  |  {4} | -b 0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0|
| d3 |  {4} | a  0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   a2d 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0   0   d3 0  0  0  |, {|
| 0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0   0   0  d3 0  0  |  {|
| 0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2 0   0  0  d3 0  |  {|
| 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0   cd2 0  0  0  d3 |  {|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|b2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0 |
|   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0 |
|   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0 |
|   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   ac|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2} | -b2 -ac -bd -c2 a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   |
|3} | c   d   0   0   0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   |
|3} | a   b   -c  -d  0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d |
|3} | 0   0   a   b   0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0   0  |
|  0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0   0  |
|  0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc2 0  |
|d 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0   bc2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0|
|0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0|
|0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   a|
|a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0   0   |
| 0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0   0   |
| 0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2 0   |
| 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0   cd2 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0 |
|   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0 |
|cd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc|
|   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d3 0  0  0  |)                                                               |
|0  d3 0  0  |                                                                |
|0  0  d3 0  |                                                                |
|0  0  0  d3 |                                                                |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0  |
|  0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0  |
|2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2|
|  bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-------------------+---------------------------------------------------------|
|                   |subquotient ({5} | 0 0 0 0 0 0 a2 ab ac ad b2 bc bd c2 cd|
|                   |                                                         |
|                   |{-1, 4}                                                  |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|-------------------+---------------------------------------------------------|
| 0   d3 0  0  0  |)|subquotient ({4} | d  ad  0 0 -bd 0 0 0 0 -cd 0 0 0 0 0 0|
| 0   0  d3 0  0  | |             {4} | -c -ac 0 0 bc  0 0 0 0 c2  0 0 0 0 0 0|
| 0   0  0  d3 0  | |             {4} | -b -ab 0 0 b2  0 0 0 0 bc  0 0 0 0 0 0|
| cd2 0  0  0  d3 | |             {4} | a  a2  0 0 -ab 0 0 0 0 -ac 0 0 0 0 0 0|
|                   |                                                         |
|                   |{-1, 3}                                                  |
|-------------------+---------------------------------------------------------|
|                   |subquotient ({2} | 0 0 b2 bd 0 bd 0 ac ac c2 0 0 0      0|
|                   |             {3} | 0 0 -c 0  0 0  0 -d -d 0  0 0 -cd    -|
|                   |             {3} | 0 0 -a c  0 c  0 -b -b d  0 0 -bc-ad -|
|                   |             {3} | 0 0 0  -a 0 -a 0 0  0  -b 0 0 ab     a|
|                   |                                                         |
|                   |{-1, 2}                                                  |
|-------------------+---------------------------------------------------------|
|                   |subquotient (| a b c d bc-ad b3-a2c ac2-b2d c3-bd2 a2 ab |
|                   |                                                         |
|                   |{-1, 1}                                                  |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|-------------------+---------------------------------------------------------|
|                   |0                                                        |
|                   |                                                         |
|                   |{-1, 0}                                                  |
|-------------------+---------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| d2 |, {5} | a2 ab ac ad b2 bc bd c2 cd d2 |)                                |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0 0 0 0 0 0 0 0 0 d  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0|
| 0 0 0 0 0 0 0 0 0 -c 0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0|
| 0 0 0 0 0 0 0 0 0 -b 0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b|
| 0 0 0 0 0 0 0 0 0 a  0  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|      0 0 0 0 0 0 0 0 0 0 0 0 0 -b2 -ac -bd -c2 a2 0  0  0  ab 0  0  0  ac 0 |
|cd    0 0 0 0 0 0 0 0 0 0 0 0 0 c   d   0   0   0  a2 0  0  0  ab 0  0  0  ac|
|bc-ad 0 0 0 0 0 0 0 0 0 0 0 0 0 a   b   -c  -d  0  0  a2 0  0  0  ab 0  0  0 |
|b     0 0 0 0 0 0 0 0 0 0 0 0 0 0   0   a   b   0  0  0  a2 0  0  0  ab 0  0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|ac ad b2 bc bd c2 cd d2 |, | bc-ad b3-a2c ac2-b2d c3-bd2 a2 ab ac ad b2 bc bd|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |, {4} | d  |
|  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |  {4} | -c |
|2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |  {4} | -b |
|  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |  {4} | a  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0|
| 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0|
| ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0|
| 0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  c|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| c2 cd d2 |)                                                                 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0 |
|0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd|
|0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0 |
|0  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  d2 0  0  0  |, {2} | -b2 -ac -bd -c2 a2 0  0  0  ab 0  0  0  ac 0  0  0  ad|
|  0  d2 0  0  |  {3} | c   d   0   0   0  a2 0  0  0  ab 0  0  0  ac 0  0  0 |
|  0  0  d2 0  |  {3} | a   b   -c  -d  0  0  a2 0  0  0  ab 0  0  0  ac 0  0 |
|d 0  0  0  d2 |  {3} | 0   0   a   b   0  0  0  a2 0  0  0  ab 0  0  0  ac 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |)                                |
| 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |                                 |
| bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |                                 |
| 0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |                                 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0|
| ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0|
| 0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d|
| 0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-------+---------------------------------------------------------------------|
|       |0                                                                    |
|       |                                                                     |
|       |{0, 4}                                                               |
|       |                                                                     |
|       |                                                                     |
|       |                                                                     |
|-------+---------------------------------------------------------------------|
|       |subquotient ({5} | a b c d |, {5} | a b c d |)                       |
|       |                                                                     |
|       |{0, 3}                                                               |
|       |                                                                     |
|       |                                                                     |
|       |                                                                     |
|-------+---------------------------------------------------------------------|
|  0  |)|subquotient ({4} | d  d  a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 |, {4} | d  |
|  0  | |             {4} | -c -c 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 |  {4} | -c |
|2 0  | |             {4} | -b -b 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 |  {4} | -b |
|  d2 | |             {4} | a  a  0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d |  {4} | a  |
|       |                                                                     |
|       |{0, 2}                                                               |
|-------+---------------------------------------------------------------------|
|       |subquotient ({2} | ac b2 c2 bd -b2 -ac -bd -c2 a 0 0 0 b 0 0 0 c 0 0 |
|       |             {3} | -d -c 0  0  c   d   0   0   0 a 0 0 0 b 0 0 0 c 0 |
|       |             {3} | -b -a d  c  a   b   -c  -d  0 0 a 0 0 0 b 0 0 0 c |
|       |             {3} | 0  0  -b -a 0   0   a   b   0 0 0 a 0 0 0 b 0 0 0 |
|       |                                                                     |
|       |{0, 1}                                                               |
|-------+---------------------------------------------------------------------|
|       |cokernel | bc-ad b3-a2c ac2-b2d c3-bd2 a b c d |                     |
|       |                                                                     |
|       |{0, 0}                                                               |
|-------+---------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|---------------------------------------------------------------------+       |
|                                                                     |       |
|                                                                     |       |
|                                                                     |       |
|                                                                     |       |
|                                                                     |       |
|                                                                     |       |
|---------------------------------------------------------------------+       |
|                                                                     |       |
|                                                                     |       |
|                                                                     |       |
|                                                                     |       |
|                                                                     |       |
|                                                                     |       |
|---------------------------------------------------------------------+       |
|a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 |)                                   |       |
|0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 |                                    |       |
|0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 |                                    |       |
|0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d |                                    |       |
|                                                                     |       |
|                                                                     |       |
|---------------------------------------------------------------------+       |
|0 d 0 0 0 |, {2} | -b2 -ac -bd -c2 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 |)|       |
|0 0 d 0 0 |  {3} | c   d   0   0   0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 | |       |
|0 0 0 d 0 |  {3} | a   b   -c  -d  0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 | |       |
|c 0 0 0 d |  {3} | 0   0   a   b   0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d | |       |
|                                                                     |       |
|                                                                     |       |
|---------------------------------------------------------------------+       |
|                                                                     |       |
|                                                                     |       |
|                                                                     |       |
|---------------------------------------------------------------------+       |
+-----------------------------------------------------------------------------+

See also
========

  * SpectralSequence _ ZZ -- the kth page of a
    spectral sequence
  * Examples of filtered complexes and spectral sequences
    -- How to use this package

Ways to use this method:
========================

  * SpectralSequence ^ ZZ -- the kth page of a
    spectral sequence
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:3480:0.

SpectralSequence _ ZZ -- the kth page of a spectral sequence
************************************************************

  * Operator: _ (Macaulay2Doc),
  * Usage:
        P = E_k
  * Inputs:
      * E, a spectral sequence,
      * k, an integer (Macaulay2Doc),
  * Outputs:
      * P, a spectral sequence page,

Description
===========

Returns the kth page of the spectral sequence determined by K.

Consider the filtered complex $K$ below, obtained by multiplying the minimal
free resolution of the rational quartic space curve by successive powers of the
irrelevant ideal.

+----------------------------------------------------+
|i1 : B = QQ[a..d];                                  |
+----------------------------------------------------+
|i2 : J = ideal vars B;                              |
|                                                    |
|o2 : Ideal of B                                     |
+----------------------------------------------------+
|i3 : C = complete res monomialCurveIdeal(B,{1,3,4});|
+----------------------------------------------------+
|i4 : K = filteredComplex(J,C,4);                    |
+----------------------------------------------------+

Let $E$ be the spectral sequence determined by $K$.

+----------------------------+
|i5 : E = spectralSequence K;|
+----------------------------+

We now compute some pages.

+-----------------------------------------------------------------------------+
|i6 : E_0                                                                     |
|                                                                             |
|     +-----------------------------------------------------------------------|
|o6 = |image | a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab2d abc2|
|     |                                                                       |
|     |{-4, 4}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 3}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 2}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 1}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 0}                                                                |
|     +-----------------------------------------------------------------------|
|                                                                             |
|o6 : SpectralSequencePage                                                    |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 bd3 c4 c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|--------------------------+--------------------------------------------------|
|3d c2d2 cd3 d4 0 0 0 0 0 ||subquotient ({2} | a3 0  0  0  a2b 0   0   0   a2c|
|                          |             {3} | 0  a3 0  0  0   a2b 0   0   0  |
|                          |             {3} | 0  0  a3 0  0   0   a2b 0   0  |
|                          |             {3} | 0  0  0  a3 0   0   0   a2b 0  |
|                          |                                                  |
|                          |{-3, 4}                                           |
|--------------------------+--------------------------------------------------|
|                          |subquotient (| a3 a2b a2c a2d ab2 abc abd ac2 acd |
|                          |                                                  |
|                          |{-3, 3}                                           |
|                          |                                                  |
|                          |                                                  |
|                          |                                                  |
|--------------------------+--------------------------------------------------|
|                          |0                                                 |
|                          |                                                  |
|                          |{-3, 2}                                           |
|                          |                                                  |
|                          |                                                  |
|                          |                                                  |
|--------------------------+--------------------------------------------------|
|                          |0                                                 |
|                          |                                                  |
|                          |{-3, 1}                                           |
|                          |                                                  |
|                          |                                                  |
|                          |                                                  |
|--------------------------+--------------------------------------------------|
|                          |0                                                 |
|                          |                                                  |
|                          |{-3, 0}                                           |
|--------------------------+--------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   |
| a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   |
| 0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   |
| 0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|ad2 b3 b2c b2d bc2 bcd bd2 c3 c2d cd2 d3 a4bc-a5d a4b3-a6c a5c2-a4b2d a4c3-a4|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|ac2 0   0   0   acd 0   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b|
|0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0|
|0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0|
|0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bd2 a3b2c-a4bd a3b4-a5bc a4bc2-a3b3d a3bc3-a3b2d2 a3bc2-a4cd a3b3c-a5c2 a4c3-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2|
|   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0 |
|   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0 |
|   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a3b2cd a3c4-a3bcd2 a3bcd-a4d2 a3b3d-a5cd a4c2d-a3b2d2 a3c3d-a3bd3 a2b3c-a3b2d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d 0   0   0   cd2 0   0   0   d3 0  0  0  -a4b2 -a5c -a4bd -a4c2 -a3b3 -a4bc |
|  c2d 0   0   0   cd2 0   0   0  d3 0  0  a4c   a4d  0     0     a3bc  a3bd  |
|  0   c2d 0   0   0   cd2 0   0  0  d3 0  a5    a4b  -a4c  -a4d  a4b   a3b2  |
|  0   0   c2d 0   0   0   cd2 0  0  0  d3 0     0    a5    a4b   0     0     |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| a2b5-a4b2c a3b2c2-a2b4d a2b2c3-a2b3d2 a2b2c2-a3bcd a2b4c-a4bc2 a3bc3-a2b3cd |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-a3b2d -a3bc2 -a3b2c -a4c2 -a3bcd -a3c3 -a3b2d -a4cd -a3bd2 -a3c2d -a2b4 -a3b|
|0      0      a3c2   a3cd  0      0     a3cd   a3d2  0      0      a2b2c a2b2|
|-a3bc  -a3bd  a4c    a3bc  -a3c2  -a3cd a4d    a3bd  -a3cd  -a3d2  a3b2  a2b3|
|a4b    a3b2   0      0     a4c    a3bc  0      0     a4d    a3bd   0     0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a2bc4-a2b2cd2 a2b2cd-a3bd2 a2b4d-a4bcd a3bc2d-a2b3d2 a2bc3d-a2b2d3 a2bc3-a3c2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2c -a2b3d -a2b2c2 -a2b3c -a3bc2 -a2b2cd -a2bc3 -a2b3d -a3bcd -a2b2d2 -a2bc2d |
|d  0      0       a2bc2  a2bcd  0       0      a2bcd  a2bd2  0       0       |
|   -a2b2c -a2b2d  a3bc   a2b2c  -a2bc2  -a2bcd a3bd   a2b2d  -a2bcd  -a2bd2  |
|   a3b2   a2b3    0      0      a3bc    a2b2c  0      0      a3bd    a2b2d   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d a2b3c2-a4c3 a3c4-a2b2c2d a2c5-a2bc2d2 a2bc2d-a3cd2 a2b3cd-a4c2d a3c3d-a2b2c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-a2b2c2 -a3c3 -a2bc2d -a2c4  -a2b2cd -a3c2d -a2bcd2 -a2c3d -a2b2d2 -a3cd2 -a2|
|a2c3    a2c2d 0       0      a2c2d   a2cd2  0       0      a2cd2   a2d3   0  |
|a3c2    a2bc2 -a2c3   -a2c2d a3cd    a2bcd  -a2c2d  -a2cd2 a3d2    a2bd2  -a2|
|0       0     a3c2    a2bc2  0       0      a3cd    a2bcd  0       0      a3d|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2 a2c4d-a2bcd3 a2bcd2-a3d3 a2b3d2-a4cd2 a3c2d2-a2b2d3 a2c3d2-a2bd4 ab4c-a2b3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|bd3 -a2c2d2 -ab5 -a2b3c -ab4d -ab3c2 -ab4c -a2b2c2 -ab3cd -ab2c3 -ab4d -a2b2c|
|    0       ab3c ab3d   0     0      ab2c2 ab2cd   0      0      ab2cd ab2d2 |
|cd2 -a2d3   a2b3 ab4    -ab3c -ab3d  a2b2c ab3c    -ab2c2 -ab2cd a2b2d ab3d  |
|2   a2bd2   0    0      a2b3  ab4    0     0       a2b2c  ab3c   0     0     |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d ab6-a3b3c a2b3c2-ab5d ab3c3-ab4d2 ab3c2-a2b2cd ab5c-a3b2c2 a2b2c3-ab4cd ab2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d -ab3d2 -ab2c2d -ab3c2 -a2bc3 -ab2c2d -abc4  -ab3cd -a2bc2d -ab2cd2 -abc3d -|
|  0      0       abc3   abc2d  0       0      abc2d  abcd2   0       0      a|
|  -ab2cd -ab2d2  a2bc2  ab2c2  -abc3   -abc2d a2bcd  ab2cd   -abc2d  -abcd2 a|
|  a2b2d  ab3d    0      0      a2bc2   ab2c2  0      0       a2bcd   ab2cd  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c4-ab3cd2 ab3cd-a2b2d2 ab5d-a3b2cd a2b2c2d-ab4d2 ab2c3d-ab3d3 ab2c3-a2bc2d ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|ab3d2 -a2bcd2 -ab2d3 -abc2d2 -ab2c3 -a2c4 -abc3d -ac5  -ab2c2d -a2c3d -abc2d2|
|bcd2  abd3    0      0       ac4    ac3d  0      0     ac3d    ac2d2  0      |
|2bd2  ab2d2   -abcd2 -abd3   a2c3   abc3  -ac4   -ac3d a2c2d   abc2d  -ac3d  |
|      0       a2bd2  ab2d2   0      0     a2c3   abc3  0       0      a2c2d  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|4c2-a3bc3 a2bc4-ab3c2d abc5-ab2c2d2 ab2c2d-a2bcd2 ab4cd-a3bc2d a2bc3d-ab3cd2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| -ac4d  -ab2cd2 -a2c2d2 -abcd3 -ac3d2 -ab2d3 -a2cd3 -abd4 -ac2d3 -b6 -ab4c -b|
| 0      ac2d2   acd3    0      0      acd3   ad4    0     0      b4c b4d   0 |
| -ac2d2 a2cd2   abcd2   -ac2d2 -acd3  a2d3   abd3   -acd3 -ad4   ab4 b5    -b|
| abc2d  0       0       a2cd2  abcd2  0      0      a2d3  abd3   0   0     ab|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|abc4d-ab2cd3 ab2cd2-a2bd3 ab4d2-a3bcd2 a2bc2d2-ab3d3 abc3d2-ab2d4 abc4-a2c3d |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|5d -b4c2 -b5c -ab3c2 -b4cd -b3c3 -b5d -ab3cd -b4d2 -b3c2d -b4c2 -ab2c3 -b3c2d|
|   0     b3c2 b3cd   0     0     b3cd b3d2   0     0      b2c3  b2c2d  0     |
|4c -b4d  ab3c b4c    -b3c2 -b3cd ab3d b4d    -b3cd -b3d2  ab2c2 b3c2   -b2c3 |
|4  b5    0    0      ab3c  b4c   0    0      ab3d  b4d    0     0      ab2c2 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|ab3c3-a3c4 a2c5-ab2c3d ac6-abc3d2 abc3d-a2c2d2 ab3c2d-a3c3d a2c4d-ab2c2d2 ac5|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| -b2c4  -b4cd -ab2c2d -b3cd2 -b2c3d -b4d2 -ab2cd2 -b3d3  -b2c2d2 -b3c3 -abc4 |
| 0      b2c2d b2cd2   0      0      b2cd2 b2d3    0      0       bc4   bc3d  |
| -b2c2d ab2cd b3cd    -b2c2d -b2cd2 ab2d2 b3d2    -b2cd2 -b2d3   abc3  b2c3  |
| b3c2   0     0       ab2cd  b3cd   0     0       ab2d2  b3d2    0     0     |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d-abc2d3 abc2d2-a2cd3 ab3cd2-a3c2d2 a2c3d2-ab2cd3 ac4d2-abcd4 abcd3-a2d4 ab3d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-b2c3d -bc5  -b3c2d -abc3d -b2c2d2 -bc4d  -b3cd2 -abc2d2 -b2cd3 -bc3d2 -b3d3 |
|0      0     bc3d   bc2d2  0       0      bc2d2  bcd3    0      0      bcd3  |
|-bc4   -bc3d abc2d  b2c2d  -bc3d   -bc2d2 abcd2  b2cd2   -bc2d2 -bcd3  abd3  |
|abc3   b2c3  0      0      abc2d   b2c2d  0      0       abcd2  b2cd2  0     |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3-a3cd3 a2c2d3-ab2d4 ac3d3-abd5 b5c-ab4d b7-a2b4c ab4c2-b6d b4c3-b5d2 b4c2-ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-abcd3 -b2d4 -bc2d3 -b2c4 -ac5 -bc4d -c6  -b2c3d -ac4d -bc3d2 -c5d  -b2c2d2 -|
|bd4    0     0      c5    c4d  0     0    c4d    c3d2  0      0     c3d2    c|
|b2d3   -bcd3 -bd4   ac4   bc4  -c5   -c4d ac3d   bc3d  -c4d   -c3d2 ac2d2   b|
|0      abd3  b2d3   0     0    ac4   bc4  0      0     ac3d   bc3d  0       0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3cd b6c-a2b3c2 ab3c3-b5cd b3c4-b4cd2 b4cd-ab3d2 b6d-a2b3cd ab3c2d-b5d2 b3c3d-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|ac3d2 -bc2d3 -c4d2 -b2cd3 -ac2d3 -bcd4 -c3d3 -b2d4 -acd4 -bd5 -c2d4 a4 0  0  |
|2d3   0      0     c2d3   cd4    0     0     cd4   d5    0    0     0  a4 0  |
|c2d2  -c3d2  -c2d3 acd3   bcd3   -c2d3 -cd4  ad4   bd4   -cd4 -d5   0  0  a4 |
|      ac2d2  bc2d2 0      0      acd3  bcd3  0     0     ad4  bd4   0  0  0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b4d3 b3c3-ab2c2d b5c2-a2b2c3 ab2c4-b4c2d b2c5-b3c2d2 b3c2d-ab2cd2 b5cd-a2b2c2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0  a3b 0   0   0   a3c 0   0   0   a3d 0   0   0   a2b2 0    0    0    a2bc 0|
|0  0   a3b 0   0   0   a3c 0   0   0   a3d 0   0   0    a2b2 0    0    0    a|
|0  0   0   a3b 0   0   0   a3c 0   0   0   a3d 0   0    0    a2b2 0    0    0|
|a4 0   0   0   a3b 0   0   0   a3c 0   0   0   a3d 0    0    0    a2b2 0    0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d ab2c3d-b4cd2 b2c4d-b3cd3 b3cd2-ab2d3 b5d2-a2b2cd2 ab2c2d2-b4d3 b2c3d2-b3d4 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d|
|2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0  |
|    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0  |
|    0    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b2c4-abc3d b4c3-a2bc4 abc5-b3c3d bc6-b2c3d2 b2c3d-abc2d2 b4c2d-a2bc3d abc4d-b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2 0    0    0    ab3 0   0   0   ab2c 0    0    0    ab2d 0    0    0    abc2|
|  a2d2 0    0    0   ab3 0   0   0    ab2c 0    0    0    ab2d 0    0    0   |
|  0    a2d2 0    0   0   ab3 0   0    0    ab2c 0    0    0    ab2d 0    0   |
|  0    0    a2d2 0   0   0   ab3 0    0    0    ab2c 0    0    0    ab2d 0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3c2d2 bc5d-b2c2d3 b2c2d2-abcd3 b4cd2-a2bc2d2 abc3d2-b3cd3 bc4d2-b2cd4 b2cd3-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0    0    0    abcd 0    0    0    abd2 0    0    0    ac3 0   0   0   ac2d |
| abc2 0    0    0    abcd 0    0    0    abd2 0    0    0   ac3 0   0   0    |
| 0    abc2 0    0    0    abcd 0    0    0    abd2 0    0   0   ac3 0   0    |
| 0    0    abc2 0    0    0    abcd 0    0    0    abd2 0   0   0   ac3 0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bd4 b4d3-a2bcd3 abc2d3-b3d4 bc3d3-b2d5 bc5-ac4d b3c4-a2c5 ac6-b2c4d c7-bc4d2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0    0    0    acd2 0    0    0    ad3 0   0   0   b4 0  0  0  b3c 0   0   0 |
|ac2d 0    0    0    acd2 0    0    0   ad3 0   0   0  b4 0  0  0   b3c 0   0 |
|0    ac2d 0    0    0    acd2 0    0   0   ad3 0   0  0  b4 0  0   0   b3c 0 |
|0    0    ac2d 0    0    0    acd2 0   0   0   ad3 0  0  0  b4 0   0   0   b3|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bc4d-ac3d2 b3c3d-a2c4d ac5d-b2c3d2 c6d-bc3d3 bc3d2-ac2d3 b3c2d2-a2c3d2 ac4d2-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  b3d 0   0   0   b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0   |
|  0   b3d 0   0   0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0   |
|  0   0   b3d 0   0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0   |
|c 0   0   0   b3d 0    0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b2c2d3 c5d2-bc2d4 bc2d3-acd4 b3cd3-a2c2d3 ac3d3-b2cd4 c4d3-bcd5 bcd4-ad5 b3d4|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| bc3 0   0   0   bc2d 0    0    0    bcd2 0    0    0    bd3 0   0   0   c4 0|
| 0   bc3 0   0   0    bc2d 0    0    0    bcd2 0    0    0   bd3 0   0   0  c|
| 0   0   bc3 0   0    0    bc2d 0    0    0    bcd2 0    0   0   bd3 0   0  0|
| 0   0   0   bc3 0    0    0    bc2d 0    0    0    bcd2 0   0   0   bd3 0  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-a2cd4 ac2d4-b2d5 c3d4-bd6 a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  0  0  c3d 0   0   0   c2d2 0    0    0    cd3 0   0   0   d4 0  0  0  |, {2|
|4 0  0  0   c3d 0   0   0    c2d2 0    0    0   cd3 0   0   0  d4 0  0  |  {3|
|  c4 0  0   0   c3d 0   0    0    c2d2 0    0   0   cd3 0   0  0  d4 0  |  {3|
|  0  c4 0   0   0   c3d 0    0    0    c2d2 0   0   0   cd3 0  0  0  d4 |  {3|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b2c ab2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|} | -a4b2 -a5c -a4bd -a4c2 -a3b3 -a4bc -a3b2d -a3bc2 -a3b2c -a4c2 -a3bcd -a3c|
|} | a4c   a4d  0     0     a3bc  a3bd  0      0      a3c2   a3cd  0      0   |
|} | a5    a4b  -a4c  -a4d  a4b   a3b2  -a3bc  -a3bd  a4c    a3bc  -a3c2  -a3c|
|} | 0     0    a5    a4b   0     0     a4b    a3b2   0      0     a4c    a3bc|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bcd2 bd3 c4 c3d c2d2 cd3 d4 |, | a4bc-a5d a4b3-a6c a5c2-a4b2d a4c3-a4bd2 a3b2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|3 -a3b2d -a4cd -a3bd2 -a3c2d -a2b4 -a3b2c -a2b3d -a2b2c2 -a2b3c -a3bc2 -a2b2c|
|  a3cd   a3d2  0      0      a2b2c a2b2d  0      0       a2bc2  a2bcd  0     |
|d a4d    a3bd  -a3cd  -a3d2  a3b2  a2b3   -a2b2c -a2b2d  a3bc   a2b2c  -a2bc2|
|  0      0     a4d    a3bd   0     0      a3b2   a2b3    0      0      a3bc  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c-a4bd a3b4-a5bc a4bc2-a3b3d a3bc3-a3b2d2 a3bc2-a4cd a3b3c-a5c2 a4c3-a3b2cd a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d -a2bc3 -a2b3d -a3bcd -a2b2d2 -a2bc2d -a2b2c2 -a3c3 -a2bc2d -a2c4  -a2b2cd -|
|  0      a2bcd  a2bd2  0       0       a2c3    a2c2d 0       0      a2c2d   a|
|  -a2bcd a3bd   a2b2d  -a2bcd  -a2bd2  a3c2    a2bc2 -a2c3   -a2c2d a3cd    a|
|  a2b2c  0      0      a3bd    a2b2d   0       0     a3c2    a2bc2  0       0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3c4-a3bcd2 a3bcd-a4d2 a3b3d-a5cd a4c2d-a3b2d2 a3c3d-a3bd3 a2b3c-a3b2d a2b5-a4|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|a3c2d -a2bcd2 -a2c3d -a2b2d2 -a3cd2 -a2bd3 -a2c2d2 -ab5 -a2b3c -ab4d -ab3c2 -|
|2cd2  0       0      a2cd2   a2d3   0      0       ab3c ab3d   0     0      a|
|2bcd  -a2c2d  -a2cd2 a3d2    a2bd2  -a2cd2 -a2d3   a2b3 ab4    -ab3c -ab3d  a|
|      a3cd    a2bcd  0       0      a3d2   a2bd2   0    0      a2b3  ab4    0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b2c a3b2c2-a2b4d a2b2c3-a2b3d2 a2b2c2-a3bcd a2b4c-a4bc2 a3bc3-a2b3cd a2bc4-a2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|ab4c -a2b2c2 -ab3cd -ab2c3 -ab4d -a2b2cd -ab3d2 -ab2c2d -ab3c2 -a2bc3 -ab2c2d|
|b2c2 ab2cd   0      0      ab2cd ab2d2   0      0       abc3   abc2d  0      |
|2b2c ab3c    -ab2c2 -ab2cd a2b2d ab3d    -ab2cd -ab2d2  a2bc2  ab2c2  -abc3  |
|     0       a2b2c  ab3c   0     0       a2b2d  ab3d    0      0      a2bc2  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b2cd2 a2b2cd-a3bd2 a2b4d-a4bcd a3bc2d-a2b3d2 a2bc3d-a2b2d3 a2bc3-a3c2d a2b3c2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| -abc4  -ab3cd -a2bc2d -ab2cd2 -abc3d -ab3d2 -a2bcd2 -ab2d3 -abc2d2 -ab2c3 -a|
| 0      abc2d  abcd2   0       0      abcd2  abd3    0      0       ac4    ac|
| -abc2d a2bcd  ab2cd   -abc2d  -abcd2 a2bd2  ab2d2   -abcd2 -abd3   a2c3   ab|
| ab2c2  0      0       a2bcd   ab2cd  0      0       a2bd2  ab2d2   0      0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-a4c3 a3c4-a2b2c2d a2c5-a2bc2d2 a2bc2d-a3cd2 a2b3cd-a4c2d a3c3d-a2b2cd2 a2c4d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2c4 -abc3d -ac5  -ab2c2d -a2c3d -abc2d2 -ac4d  -ab2cd2 -a2c2d2 -abcd3 -ac3d2 |
|3d  0      0     ac3d    ac2d2  0       0      ac2d2   acd3    0      0      |
|c3  -ac4   -ac3d a2c2d   abc2d  -ac3d   -ac2d2 a2cd2   abcd2   -ac2d2 -acd3  |
|    a2c3   abc3  0       0      a2c2d   abc2d  0       0       a2cd2  abcd2  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-a2bcd3 a2bcd2-a3d3 a2b3d2-a4cd2 a3c2d2-a2b2d3 a2c3d2-a2bd4 ab4c-a2b3d ab6-a3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-ab2d3 -a2cd3 -abd4 -ac2d3 -b6 -ab4c -b5d -b4c2 -b5c -ab3c2 -b4cd -b3c3 -b5d |
|acd3   ad4    0     0      b4c b4d   0    0     b3c2 b3cd   0     0     b3cd |
|a2d3   abd3   -acd3 -ad4   ab4 b5    -b4c -b4d  ab3c b4c    -b3c2 -b3cd ab3d |
|0      0      a2d3  abd3   0   0     ab4  b5    0    0      ab3c  b4c   0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b3c a2b3c2-ab5d ab3c3-ab4d2 ab3c2-a2b2cd ab5c-a3b2c2 a2b2c3-ab4cd ab2c4-ab3cd|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-ab3cd -b4d2 -b3c2d -b4c2 -ab2c3 -b3c2d -b2c4  -b4cd -ab2c2d -b3cd2 -b2c3d -b|
|b3d2   0     0      b2c3  b2c2d  0      0      b2c2d b2cd2   0      0      b2|
|b4d    -b3cd -b3d2  ab2c2 b3c2   -b2c3  -b2c2d ab2cd b3cd    -b2c2d -b2cd2 ab|
|0      ab3d  b4d    0     0      ab2c2  b3c2   0     0       ab2cd  b3cd   0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2 ab3cd-a2b2d2 ab5d-a3b2cd a2b2c2d-ab4d2 ab2c3d-ab3d3 ab2c3-a2bc2d ab4c2-a3bc|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|4d2 -ab2cd2 -b3d3  -b2c2d2 -b3c3 -abc4 -b2c3d -bc5  -b3c2d -abc3d -b2c2d2 -bc|
|cd2 b2d3    0      0       bc4   bc3d  0      0     bc3d   bc2d2  0       0  |
|2d2 b3d2    -b2cd2 -b2d3   abc3  b2c3  -bc4   -bc3d abc2d  b2c2d  -bc3d   -bc|
|    0       ab2d2  b3d2    0     0     abc3   b2c3  0      0      abc2d   b2c|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3 a2bc4-ab3c2d abc5-ab2c2d2 ab2c2d-a2bcd2 ab4cd-a3bc2d a2bc3d-ab3cd2 abc4d-ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|4d  -b3cd2 -abc2d2 -b2cd3 -bc3d2 -b3d3 -abcd3 -b2d4 -bc2d3 -b2c4 -ac5 -bc4d -|
|    bc2d2  bcd3    0      0      bcd3  bd4    0     0      c5    c4d  0     0|
|2d2 abcd2  b2cd2   -bc2d2 -bcd3  abd3  b2d3   -bcd3 -bd4   ac4   bc4  -c5   -|
|2d  0      0       abcd2  b2cd2  0     0      abd3  b2d3   0     0    ac4   b|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2cd3 ab2cd2-a2bd3 ab4d2-a3bcd2 a2bc2d2-ab3d3 abc3d2-ab2d4 abc4-a2c3d ab3c3-a3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c6  -b2c3d -ac4d -bc3d2 -c5d  -b2c2d2 -ac3d2 -bc2d3 -c4d2 -b2cd3 -ac2d3 -bcd4|
|    c4d    c3d2  0      0     c3d2    c2d3   0      0     c2d3   cd4    0    |
|c4d ac3d   bc3d  -c4d   -c3d2 ac2d2   bc2d2  -c3d2  -c2d3 acd3   bcd3   -c2d3|
|c4  0      0     ac3d   bc3d  0       0      ac2d2  bc2d2 0      0      acd3 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c4 a2c5-ab2c3d ac6-abc3d2 abc3d-a2c2d2 ab3c2d-a3c3d a2c4d-ab2c2d2 ac5d-abc2d3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| -c3d3 -b2d4 -acd4 -bd5 -c2d4 a4 0  0  0  a3b 0   0   0   a3c 0   0   0   a3d|
| 0     cd4   d5    0    0     0  a4 0  0  0   a3b 0   0   0   a3c 0   0   0  |
| -cd4  ad4   bd4   -cd4 -d5   0  0  a4 0  0   0   a3b 0   0   0   a3c 0   0  |
| bcd3  0     0     ad4  bd4   0  0  0  a4 0   0   0   a3b 0   0   0   a3c 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| abc2d2-a2cd3 ab3cd2-a3c2d2 a2c3d2-ab2cd3 ac4d2-abcd4 abcd3-a2d4 ab3d3-a3cd3 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   0   0   a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    a2c2|
| a3d 0   0   0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0   |
| 0   a3d 0   0    0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0   |
| 0   0   a3d 0    0    0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a2c2d3-ab2d4 ac3d3-abd5 b5c-ab4d b7-a2b4c ab4c2-b6d b4c3-b5d2 b4c2-ab3cd b6c-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0    0    0    a2cd 0    0    0    a2d2 0    0    0    ab3 0   0   0   ab2c |
| a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0    0   ab3 0   0   0    |
| 0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0   0   ab3 0   0    |
| 0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0   0   0   ab3 0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a2b3c2 ab3c3-b5cd b3c4-b4cd2 b4cd-ab3d2 b6d-a2b3cd ab3c2d-b5d2 b3c3d-b4d3 b3c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0    ab|
|ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0 |
|0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0 |
|0    0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3-ab2c2d b5c2-a2b2c3 ab2c4-b4c2d b2c5-b3c2d2 b3c2d-ab2cd2 b5cd-a2b2c2d ab2c3d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d2 0    0    0    ac3 0   0   0   ac2d 0    0    0    acd2 0    0    0    ad3|
|   abd2 0    0    0   ac3 0   0   0    ac2d 0    0    0    acd2 0    0    0  |
|   0    abd2 0    0   0   ac3 0   0    0    ac2d 0    0    0    acd2 0    0  |
|   0    0    abd2 0   0   0   ac3 0    0    0    ac2d 0    0    0    acd2 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-b4cd2 b2c4d-b3cd3 b3cd2-ab2d3 b5d2-a2b2cd2 ab2c2d2-b4d3 b2c3d2-b3d4 b2c4-abc|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   0   0   b4 0  0  0  b3c 0   0   0   b3d 0   0   0   b2c2 0    0    0    |
| ad3 0   0   0  b4 0  0  0   b3c 0   0   0   b3d 0   0   0    b2c2 0    0    |
| 0   ad3 0   0  0  b4 0  0   0   b3c 0   0   0   b3d 0   0    0    b2c2 0    |
| 0   0   ad3 0  0  0  b4 0   0   0   b3c 0   0   0   b3d 0    0    0    b2c2 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3d b4c3-a2bc4 abc5-b3c3d bc6-b2c3d2 b2c3d-abc2d2 b4c2d-a2bc3d abc4d-b3c2d2 bc|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|b2cd 0    0    0    b2d2 0    0    0    bc3 0   0   0   bc2d 0    0    0    b|
|0    b2cd 0    0    0    b2d2 0    0    0   bc3 0   0   0    bc2d 0    0    0|
|0    0    b2cd 0    0    0    b2d2 0    0   0   bc3 0   0    0    bc2d 0    0|
|0    0    0    b2cd 0    0    0    b2d2 0   0   0   bc3 0    0    0    bc2d 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|5d-b2c2d3 b2c2d2-abcd3 b4cd2-a2bc2d2 abc3d2-b3cd3 bc4d2-b2cd4 b2cd3-abd4 b4d3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|cd2 0    0    0    bd3 0   0   0   c4 0  0  0  c3d 0   0   0   c2d2 0    0   |
|    bcd2 0    0    0   bd3 0   0   0  c4 0  0  0   c3d 0   0   0    c2d2 0   |
|    0    bcd2 0    0   0   bd3 0   0  0  c4 0  0   0   c3d 0   0    0    c2d2|
|    0    0    bcd2 0   0   0   bd3 0  0  0  c4 0   0   0   c3d 0    0    0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-a2bcd3 abc2d3-b3d4 bc3d3-b2d5 bc5-ac4d b3c4-a2c5 ac6-b2c4d c7-bc4d2 bc4d-ac3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0    cd3 0   0   0   d4 0  0  0  |)                                         |
| 0    0   cd3 0   0   0  d4 0  0  |                                          |
| 0    0   0   cd3 0   0  0  d4 0  |                                          |
| c2d2 0   0   0   cd3 0  0  0  d4 |                                          |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2 b3c3d-a2c4d ac5d-b2c3d2 c6d-bc3d3 bc3d2-ac2d3 b3c2d2-a2c3d2 ac4d2-b2c2d3 c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|5d2-bc2d4 bc2d3-acd4 b3cd3-a2c2d3 ac3d3-b2cd4 c4d3-bcd5 bcd4-ad5 b3d4-a2cd4 a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2d4-b2d5 c3d4-bd6 a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab2d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 bd3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|----------------------+------------------------------------------------------|
|                      |subquotient ({4} | a2 0  0  0  ab 0  0  0  ac 0  0  0 |
|                      |             {4} | 0  a2 0  0  0  ab 0  0  0  ac 0  0 |
|                      |             {4} | 0  0  a2 0  0  0  ab 0  0  0  ac 0 |
|                      |             {4} | 0  0  0  a2 0  0  0  ab 0  0  0  ac|
|                      |                                                      |
|                      |{-2, 4}                                               |
|----------------------+------------------------------------------------------|
| c4 c3d c2d2 cd3 d4 |)|subquotient ({2} | a2 0  0  0  ab 0  0  0  ac 0  0  0 |
|                      |             {3} | 0  a2 0  0  0  ab 0  0  0  ac 0  0 |
|                      |             {3} | 0  0  a2 0  0  0  ab 0  0  0  ac 0 |
|                      |             {3} | 0  0  0  a2 0  0  0  ab 0  0  0  ac|
|                      |                                                      |
|                      |{-2, 3}                                               |
|----------------------+------------------------------------------------------|
|                      |subquotient (| a2 ab ac ad b2 bc bd c2 cd d2 a3bc-a4d |
|                      |                                                      |
|                      |{-2, 2}                                               |
|                      |                                                      |
|                      |                                                      |
|                      |                                                      |
|----------------------+------------------------------------------------------|
|                      |0                                                     |
|                      |                                                      |
|                      |{-2, 1}                                               |
|                      |                                                      |
|                      |                                                      |
|                      |                                                      |
|----------------------+------------------------------------------------------|
|                      |0                                                     |
|                      |                                                      |
|                      |{-2, 0}                                               |
|----------------------+------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0|
| 0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d|
| 0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0|
| 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0|
| 0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d|
| 0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0|
| 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a3b3-a5c a4c2-a3b2d a3c3-a3bd2 a2b2c-a3bd a2b4-a4bc a3bc2-a2b3d a2bc3-a2b2d2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  0  0  a3d  a2bd  a2cd  a2d2  ab2d  abcd  abd2  ac2d  acd2  ad3   b3d  b2cd |
|2 0  0  -a3c -a2bc -a2c2 -a2cd -ab2c -abc2 -abcd -ac3  -ac2d -acd2 -b3c -b2c2|
|  d2 0  -a3b -a2b2 -a2bc -a2bd -ab3  -ab2c -ab2d -abc2 -abcd -abd2 -b4  -b3c |
|  0  d2 a4   a3b   a3c   a3d   a2b2  a2bc  a2bd  a2c2  a2cd  a2d2  ab3  ab2c |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  0  0  -a3b2 -a4c -a3bd -a3c2 -a2b3 -a3bc -a2b2d -a2bc2 -a2b2c -a3c2 -a2bcd |
|2 0  0  a3c   a3d  0     0     a2bc  a2bd  0      0      a2c2   a2cd  0      |
|  d2 0  a4    a3b  -a3c  -a3d  a3b   a2b2  -a2bc  -a2bd  a3c    a2bc  -a2c2  |
|  0  d2 0     0    a4    a3b   0     0     a3b    a2b2   0      0     a3c    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a2bc2-a3cd a2b3c-a4c2 a3c3-a2b2cd a2c4-a2bcd2 a2bcd-a3d2 a2b3d-a4cd a3c2d-a2b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| b2d2  bc2d  bcd2  bd3   c3d  c2d2  cd3   d4   a3 0  0  0  a2b 0   0   0   a2|
| -b2cd -bc3  -bc2d -bcd2 -c4  -c3d  -c2d2 -cd3 0  a3 0  0  0   a2b 0   0   0 |
| -b3d  -b2c2 -b2cd -b2d2 -bc3 -bc2d -bcd2 -bd3 0  0  a3 0  0   0   a2b 0   0 |
| ab2d  abc2  abcd  abd2  ac3  ac2d  acd2  ad3  0  0  0  a3 0   0   0   a2b 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-a2c3 -a2b2d -a3cd -a2bd2 -a2c2d -ab4 -a2b2c -ab3d -ab2c2 -ab3c -a2bc2 -ab2cd|
|0     a2cd   a2d2  0      0      ab2c ab2d   0     0      abc2  abcd   0     |
|-a2cd a3d    a2bd  -a2cd  -a2d2  a2b2 ab3    -ab2c -ab2d  a2bc  ab2c   -abc2 |
|a2bc  0      0     a3d    a2bd   0    0      a2b2  ab3    0     0      a2bc  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2d2 a2c3d-a2bd3 ab3c-a2b2d ab5-a3b2c a2b2c2-ab4d ab2c3-ab3d2 ab2c2-a2bcd ab4c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0  |
|  a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0  |
|  0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0  |
|  0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| -abc3 -ab3d -a2bcd -ab2d2 -abc2d -ab2c2 -a2c3 -abc2d -ac4  -ab2cd -a2c2d -ab|
| 0     abcd  abd2   0      0      ac3    ac2d  0      0     ac2d   acd2   0  |
| -abcd a2bd  ab2d   -abcd  -abd2  a2c2   abc2  -ac3   -ac2d a2cd   abcd   -ac|
| ab2c  0     0      a2bd   ab2d   0      0     a2c2   abc2  0      0      a2c|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-a3bc2 a2bc3-ab3cd abc4-ab2cd2 ab2cd-a2bd2 ab4d-a3bcd a2bc2d-ab3d2 abc3d-ab2d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| ac2 0   0   0   acd 0   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   |
| 0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   |
| 0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   |
| 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|cd2 -ac3d -ab2d2 -a2cd2 -abd3 -ac2d2 -b5 -ab3c -b4d -b3c2 -b4c -ab2c2 -b3cd -|
|    0     acd2   ad3    0     0      b3c b3d   0    0     b2c2 b2cd   0     0|
|2d  -acd2 a2d2   abd2   -acd2 -ad3   ab3 b4    -b3c -b3d  ab2c b3c    -b2c2 -|
|d   abcd  0      0      a2d2  abd2   0   0     ab3  b4    0    0      ab2c  b|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3 abc3-a2c2d ab3c2-a3c3 a2c4-ab2c2d ac5-abc2d2 abc2d-a2cd2 ab3cd-a3c2d a2c3d-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c|
|0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0|
|0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0|
|0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b2c3 -b4d -ab2cd -b3d2 -b2c2d -b3c2 -abc3 -b2c2d -bc4  -b3cd -abc2d -b2cd2 -b|
|     b2cd b2d2   0     0      bc3   bc2d  0      0     bc2d  bcd2   0      0 |
|b2cd ab2d b3d    -b2cd -b2d2  abc2  b2c2  -bc3   -bc2d abcd  b2cd   -bc2d  -b|
|3c   0    0      ab2d  b3d    0     0     abc2   b2c2  0     0      abcd   b2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|ab2cd2 ac4d-abcd3 abcd2-a2d3 ab3d2-a3cd2 a2c2d2-ab2d3 ac3d2-abd4 b4c-ab3d b6-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2d 0   0   0   cd2 0   0   0   d3 0  0  0  |, {4} | a3d  a2bd  a2cd  a2d2  ab|
|   c2d 0   0   0   cd2 0   0   0  d3 0  0  |  {4} | -a3c -a2bc -a2c2 -a2cd -a|
|   0   c2d 0   0   0   cd2 0   0  0  d3 0  |  {4} | -a3b -a2b2 -a2bc -a2bd -a|
|   0   0   c2d 0   0   0   cd2 0  0  0  d3 |  {4} | a4   a3b   a3c   a3d   a2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c3d -b3d2 -abcd2 -b2d3 -bc2d2 -b2c3 -ac4 -bc3d -c5  -b2c2d -ac3d -bc2d2 -c4d |
|    bcd2  bd3    0     0      c4    c3d  0     0    c3d    c2d2  0      0    |
|cd2 abd2  b2d2   -bcd2 -bd3   ac3   bc3  -c4   -c3d ac2d   bc2d  -c3d   -c2d2|
|cd  0     0      abd2  b2d2   0     0    ac3   bc3  0      0     ac2d   bc2d |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a2b3c ab3c2-b5d b3c3-b4d2 b3c2-ab2cd b5c-a2b2c2 ab2c3-b4cd b2c4-b3cd2 b3cd-ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2d  abcd  abd2  ac2d  acd2  ad3   b3d  b2cd  b2d2  bc2d  bcd2  bd3   c3d  c2d|
|b2c -abc2 -abcd -ac3  -ac2d -acd2 -b3c -b2c2 -b2cd -bc3  -bc2d -bcd2 -c4  -c3|
|b3  -ab2c -ab2d -abc2 -abcd -abd2 -b4  -b3c  -b3d  -b2c2 -b2cd -b2d2 -bc3 -bc|
|b2  a2bc  a2bd  a2c2  a2cd  a2d2  ab3  ab2c  ab2d  abc2  abcd  abd2  ac3  ac2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| -b2cd2 -ac2d2 -bcd3 -c3d2 -b2d3 -acd3 -bd4 -c2d3 a3 0  0  0  a2b 0   0   0  |
| c2d2   cd3    0     0     cd3   d4    0    0     0  a3 0  0  0   a2b 0   0  |
| acd2   bcd2   -c2d2 -cd3  ad3   bd3   -cd3 -d4   0  0  a3 0  0   0   a2b 0  |
| 0      0      acd2  bcd2  0     0     ad3  bd3   0  0  0  a3 0   0   0   a2b|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2d2 b5d-a2b2cd ab2c2d-b4d2 b2c3d-b3d3 b2c3-abc2d b4c2-a2bc3 abc4-b3c2d bc5-b2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2  cd3   d4   a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2|
|d  -c2d2 -cd3 0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0  |
|2d -bcd2 -bd3 0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0  |
|d  acd2  ad3  0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   a2d 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   |
| 0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   |
| 0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd |
| 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2d2 b2c2d-abcd2 b4cd-a2bc2d abc3d-b3cd2 bc4d-b2cd3 b2cd2-abd3 b4d2-a2bcd2 ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   |
| ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   |
| 0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   |
| 0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0|
|0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0|
|0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0|
|abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2d2-b3d3 bc3d2-b2d4 bc4-ac3d b3c3-a2c4 ac5-b2c3d c6-bc3d2 bc3d-ac2d2 b3c2d-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   b|
|0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0|
|0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0|
|0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0   bc2 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0|
|   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0|
|   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0|
|2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2c3d ac4d-b2c2d2 c5d-bc2d3 bc2d2-acd3 b3cd2-a2c2d2 ac3d2-b2cd3 c4d2-bcd4 bcd3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|cd 0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0   0   d3|
|   bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0   0   0 |
|   0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2 0   0 |
|   0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0   cd2 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  c2d 0   0   0   cd2 0   0   0   d3 0  0  0  |, {2} | -a3b2 -a4c -a3bd -a3c2|
|  0   c2d 0   0   0   cd2 0   0   0  d3 0  0  |  {3} | a3c   a3d  0     0    |
|  0   0   c2d 0   0   0   cd2 0   0  0  d3 0  |  {3} | a4    a3b  -a3c  -a3d |
|3 0   0   0   c2d 0   0   0   cd2 0  0  0  d3 |  {3} | 0     0    a4    a3b  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-ad4 b3d3-a2cd3 ac2d3-b2d4 c3d3-bd5 a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0  0  0  |)                                                                 |
| d3 0  0  |                                                                  |
| 0  d3 0  |                                                                  |
| 0  0  d3 |                                                                  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| -a2b3 -a3bc -a2b2d -a2bc2 -a2b2c -a3c2 -a2bcd -a2c3 -a2b2d -a3cd -a2bd2 -a2c|
| a2bc  a2bd  0      0      a2c2   a2cd  0      0     a2cd   a2d2  0      0   |
| a3b   a2b2  -a2bc  -a2bd  a3c    a2bc  -a2c2  -a2cd a3d    a2bd  -a2cd  -a2d|
| 0     0     a3b    a2b2   0      0     a3c    a2bc  0      0     a3d    a2bd|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| b2c b2d bc2 bcd bd2 c3 c2d cd2 d3 |, | a3bc-a4d a3b3-a5c a4c2-a3b2d a3c3-a3b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2d -ab4 -a2b2c -ab3d -ab2c2 -ab3c -a2bc2 -ab2cd -abc3 -ab3d -a2bcd -ab2d2 -ab|
|   ab2c ab2d   0     0      abc2  abcd   0      0     abcd  abd2   0      0  |
|2  a2b2 ab3    -ab2c -ab2d  a2bc  ab2c   -abc2  -abcd a2bd  ab2d   -abcd  -ab|
|   0    0      a2b2  ab3    0     0      a2bc   ab2c  0     0      a2bd   ab2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2 a2b2c-a3bd a2b4-a4bc a3bc2-a2b3d a2bc3-a2b2d2 a2bc2-a3cd a2b3c-a4c2 a3c3-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2d -ab2c2 -a2c3 -abc2d -ac4  -ab2cd -a2c2d -abcd2 -ac3d -ab2d2 -a2cd2 -abd3 |
|    ac3    ac2d  0      0     ac2d   acd2   0      0     acd2   ad3    0     |
|d2  a2c2   abc2  -ac3   -ac2d a2cd   abcd   -ac2d  -acd2 a2d2   abd2   -acd2 |
|d   0      0     a2c2   abc2  0      0      a2cd   abcd  0      0      a2d2  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2b2cd a2c4-a2bcd2 a2bcd-a3d2 a2b3d-a4cd a3c2d-a2b2d2 a2c3d-a2bd3 ab3c-a2b2d a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-ac2d2 -b5 -ab3c -b4d -b3c2 -b4c -ab2c2 -b3cd -b2c3 -b4d -ab2cd -b3d2 -b2c2d |
|0      b3c b3d   0    0     b2c2 b2cd   0     0     b2cd b2d2   0     0      |
|-ad3   ab3 b4    -b3c -b3d  ab2c b3c    -b2c2 -b2cd ab2d b3d    -b2cd -b2d2  |
|abd2   0   0     ab3  b4    0    0      ab2c  b3c   0    0      ab2d  b3d    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b5-a3b2c a2b2c2-ab4d ab2c3-ab3d2 ab2c2-a2bcd ab4c-a3bc2 a2bc3-ab3cd abc4-ab2c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-b3c2 -abc3 -b2c2d -bc4  -b3cd -abc2d -b2cd2 -bc3d -b3d2 -abcd2 -b2d3 -bc2d2 |
|bc3   bc2d  0      0     bc2d  bcd2   0      0     bcd2  bd3    0     0      |
|abc2  b2c2  -bc3   -bc2d abcd  b2cd   -bc2d  -bcd2 abd2  b2d2   -bcd2 -bd3   |
|0     0     abc2   b2c2  0     0      abcd   b2cd  0     0      abd2  b2d2   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2 ab2cd-a2bd2 ab4d-a3bcd a2bc2d-ab3d2 abc3d-ab2d3 abc3-a2c2d ab3c2-a3c3 a2c4|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-b2c3 -ac4 -bc3d -c5  -b2c2d -ac3d -bc2d2 -c4d  -b2cd2 -ac2d2 -bcd3 -c3d2 -b2|
|c4    c3d  0     0    c3d    c2d2  0      0     c2d2   cd3    0     0     cd3|
|ac3   bc3  -c4   -c3d ac2d   bc2d  -c3d   -c2d2 acd2   bcd2   -c2d2 -cd3  ad3|
|0     0    ac3   bc3  0      0     ac2d   bc2d  0      0      acd2  bcd2  0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-ab2c2d ac5-abc2d2 abc2d-a2cd2 ab3cd-a3c2d a2c3d-ab2cd2 ac4d-abcd3 abcd2-a2d3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d3 -acd3 -bd4 -c2d3 a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   0|
|   d4    0    0     0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   0|
|   bd3   -cd3 -d4   0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d 0|
|   0     ad3  bd3   0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   a|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| ab3d2-a3cd2 a2c2d2-ab2d3 ac3d2-abd4 b4c-ab3d b6-a2b3c ab3c2-b5d b3c3-b4d2 b3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0 |
|   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0 |
|   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   ac|
|2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2-ab2cd b5c-a2b2c2 ab2c3-b4cd b2c4-b3cd2 b3cd-ab2d2 b5d-a2b2cd ab2c2d-b4d2 b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0  |
|  0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0  |
|d 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc2|
|  acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2c3d-b3d3 b2c3-abc2d b4c2-a2bc3 abc4-b3c2d bc5-b2c2d2 b2c2d-abcd2 b4cd-a2bc2d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0   |
| 0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0   |
| 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2 |
| bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| abc3d-b3cd2 bc4d-b2cd3 b2cd2-abd3 b4d2-a2bcd2 abc2d2-b3d3 bc3d2-b2d4 bc4-ac3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|0   d3 0  0  0  |)                                                           |
|0   0  d3 0  0  |                                                            |
|0   0  0  d3 0  |                                                            |
|cd2 0  0  0  d3 |                                                            |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d b3c3-a2c4 ac5-b2c3d c6-bc3d2 bc3d-ac2d2 b3c2d-a2c3d ac4d-b2c2d2 c5d-bc2d3 b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2d2-acd3 b3cd2-a2c2d2 ac3d2-b2cd3 c4d2-bcd4 bcd3-ad4 b3d3-a2cd3 ac2d3-b2d4 c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3d3-bd5 a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3 b2c b2d bc2 bcd bd2 c3 c2d |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|---------+-------------------------------------------------------------------|
|         |subquotient ({5} | a b c d a2 ab ac ad b2 bc bd c2 cd d2 |, {5} | a|
|         |                                                                   |
|         |{-1, 4}                                                            |
|         |                                                                   |
|         |                                                                   |
|         |                                                                   |
|---------+-------------------------------------------------------------------|
|         |subquotient ({4} | a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 a2d  abd  acd  a|
|         |             {4} | 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 -a2c -abc -ac2 -|
|         |             {4} | 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 -a2b -ab2 -abc -|
|         |             {4} | 0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d a3   a2b  a2c  a|
|         |                                                                   |
|         |{-1, 3}                                                            |
|---------+-------------------------------------------------------------------|
|cd2 d3 |)|subquotient ({2} | a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 -a2b2 -a3c -a2bd|
|         |             {3} | 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 a2c   a2d  0    |
|         |             {3} | 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 a3    a2b  -a2c |
|         |             {3} | 0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0     0    a3   |
|         |                                                                   |
|         |{-1, 2}                                                            |
|---------+-------------------------------------------------------------------|
|         |subquotient (| a b c d a2bc-a3d a2b3-a4c a3c2-a2b2d a2c3-a2bd2 ab2c|
|         |                                                                   |
|         |{-1, 1}                                                            |
|         |                                                                   |
|         |                                                                   |
|         |                                                                   |
|---------+-------------------------------------------------------------------|
|         |0                                                                  |
|         |                                                                   |
|         |{-1, 0}                                                            |
|---------+-------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2 ab ac ad b2 bc bd c2 cd d2 |)                                              |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2  b2d  bcd  bd2  c2d  cd2  d3   a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0|
|acd -b2c -bc2 -bcd -c3  -c2d -cd2 0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0|
|abd -b3  -b2c -b2d -bc2 -bcd -bd2 0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  a|
|2d  ab2  abc  abd  ac2  acd  ad2  0  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| -a2c2 -ab3 -a2bc -ab2d -abc2 -ab2c -a2c2 -abcd -ac3 -ab2d -a2cd -abd2 -ac2d |
| 0     abc  abd   0     0     ac2   acd   0     0    acd   ad2   0     0     |
| -a2d  a2b  ab2   -abc  -abd  a2c   abc   -ac2  -acd a2d   abd   -acd  -ad2  |
| a2b   0    0     a2b   ab2   0     0     a2c   abc  0     0     a2d   abd   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-a2bd ab4-a3bc a2bc2-ab3d abc3-ab2d2 abc2-a2cd ab3c-a3c2 a2c3-ab2cd ac4-abcd2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |
|  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |
|d 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |
|  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-b4 -ab2c -b3d -b2c2 -b3c -abc2 -b2cd -bc3 -b3d -abcd -b2d2 -bc2d -b2c2 -ac3 |
|b2c b2d   0    0     bc2  bcd   0     0    bcd  bd2   0     0     c3    c2d  |
|ab2 b3    -b2c -b2d  abc  b2c   -bc2  -bcd abd  b2d   -bcd  -bd2  ac2   bc2  |
|0   0     ab2  b3    0    0     abc   b2c  0    0     abd   b2d   0     0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| abcd-a2d2 ab3d-a3cd a2c2d-ab2d2 ac3d-abd3 b3c-ab2d b5-a2b2c ab2c2-b4d b2c3-b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
||, {4} | a2d  abd  acd  ad2  b2d  bcd  bd2  c2d  cd2  d3   a2 0  0  0  ab 0  |
||  {4} | -a2c -abc -ac2 -acd -b2c -bc2 -bcd -c3  -c2d -cd2 0  a2 0  0  0  ab |
||  {4} | -a2b -ab2 -abc -abd -b3  -b2c -b2d -bc2 -bcd -bd2 0  0  a2 0  0  0  |
||  {4} | a3   a2b  a2c  a2d  ab2  abc  abd  ac2  acd  ad2  0  0  0  a2 0  0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-bc2d -c4  -b2cd -ac2d -bcd2 -c3d -b2d2 -acd2 -bd3 -c2d2 a2 0  0  0  ab 0  0 |
|0     0    c2d   cd2   0     0    cd2   d3    0    0     0  a2 0  0  0  ab 0 |
|-c3   -c2d acd   bcd   -c2d  -cd2 ad2   bd2   -cd2 -d3   0  0  a2 0  0  0  ab|
|ac2   bc2  0     0     acd   bcd  0     0     ad2  bd2   0  0  0  a2 0  0  0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3d2 b2c2-abcd b4c-a2bc2 abc3-b3cd bc4-b2cd2 b2cd-abd2 b4d-a2bcd abc2d-b3d2 bc|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0 |
|0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0 |
|ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0 |
|0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  c|
| 0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0|
| 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0|
| ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3d-b2d3 bc3-ac2d b3c2-a2c3 ac4-b2c2d c5-bc2d2 bc2d-acd2 b3cd-a2c2d ac3d-b2cd2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| cd 0  0  0  d2 0  0  0  |)                                                  |
| 0  cd 0  0  0  d2 0  0  |                                                   |
| 0  0  cd 0  0  0  d2 0  |                                                   |
| 0  0  0  cd 0  0  0  d2 |                                                   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d 0  0  0  d2 0  0  0  |, {2} | -a2b2 -a3c -a2bd -a2c2 -ab3 -a2bc -ab2d -abc2|
|  cd 0  0  0  d2 0  0  |  {3} | a2c   a2d  0     0     abc  abd   0     0    |
|  0  cd 0  0  0  d2 0  |  {3} | a3    a2b  -a2c  -a2d  a2b  ab2   -abc  -abd |
|  0  0  cd 0  0  0  d2 |  {3} | 0     0    a3    a2b   0    0     a2b   ab2  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| c4d-bcd3 bcd2-ad3 b3d2-a2cd2 ac2d2-b2d3 c3d2-bd4 a2 ab ac ad b2 bc bd c2 cd |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| -ab2c -a2c2 -abcd -ac3 -ab2d -a2cd -abd2 -ac2d -b4 -ab2c -b3d -b2c2 -b3c -ab|
| ac2   acd   0     0    acd   ad2   0     0     b2c b2d   0    0     bc2  bcd|
| a2c   abc   -ac2  -acd a2d   abd   -acd  -ad2  ab2 b3    -b2c -b2d  abc  b2c|
| 0     0     a2c   abc  0     0     a2d   abd   0   0     ab2  b3    0    0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2 |, | a2bc-a3d a2b3-a4c a3c2-a2b2d a2c3-a2bd2 ab2c-a2bd ab4-a3bc a2bc2-ab3d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2 -b2cd -bc3 -b3d -abcd -b2d2 -bc2d -b2c2 -ac3 -bc2d -c4  -b2cd -ac2d -bcd2 |
|   0     0    bcd  bd2   0     0     c3    c2d  0     0    c2d   cd2   0     |
|   -bc2  -bcd abd  b2d   -bcd  -bd2  ac2   bc2  -c3   -c2d acd   bcd   -c2d  |
|   abc   b2c  0    0     abd   b2d   0     0    ac2   bc2  0     0     acd   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| abc3-ab2d2 abc2-a2cd ab3c-a3c2 a2c3-ab2cd ac4-abcd2 abcd-a2d2 ab3d-a3cd a2c2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-c3d -b2d2 -acd2 -bd3 -c2d2 a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b|
|0    cd2   d3    0    0     0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0|
|-cd2 ad2   bd2   -cd2 -d3   0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0|
|bcd  0     0     ad2  bd2   0  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d-ab2d2 ac3d-abd3 b3c-ab2d b5-a2b2c ab2c2-b4d b2c3-b3d2 b2c2-abcd b4c-a2bc2 a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |)    |
|  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |     |
|  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |     |
|  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |     |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bc3-b3cd bc4-b2cd2 b2cd-abd2 b4d-a2bcd abc2d-b3d2 bc3d-b2d3 bc3-ac2d b3c2-a2c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3 ac4-b2c2d c5-bc2d2 bc2d-acd2 b3cd-a2c2d ac3d-b2cd2 c4d-bcd3 bcd2-ad3 b3d2-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|---------------------------------------------------------+-------------------|
|                                                         |0                  |
|                                                         |                   |
|                                                         |{0, 4}             |
|                                                         |                   |
|                                                         |                   |
|                                                         |                   |
|---------------------------------------------------------+-------------------|
|                                                         |cokernel {5} | a b |
|                                                         |                   |
|                                                         |{0, 3}             |
|                                                         |                   |
|                                                         |                   |
|                                                         |                   |
|---------------------------------------------------------+-------------------|
|                                                         |cokernel {4} | ad  |
|                                                         |         {4} | -ac |
|                                                         |         {4} | -ab |
|                                                         |         {4} | a2  |
|                                                         |                   |
|                                                         |{0, 2}             |
|---------------------------------------------------------+-------------------|
|2cd2 ac2d2-b2d3 c3d2-bd4 a2 ab ac ad b2 bc bd c2 cd d2 |)|cokernel {2} | -ab2|
|                                                         |         {3} | ac  |
|                                                         |         {3} | a2  |
|                                                         |         {3} | 0   |
|                                                         |                   |
|                                                         |{0, 1}             |
|---------------------------------------------------------+-------------------|
|                                                         |cokernel | abc-a2d |
|                                                         |                   |
|                                                         |{0, 0}             |
|---------------------------------------------------------+-------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c d |                                                                        |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bd  cd  d2  a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 |                                |
|-bc -c2 -cd 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 |                                |
|-b2 -bc -bd 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 |                                |
|ab  ac  ad  0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d |                                |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| -a2c -abd -ac2 -b3 -abc -b2d -bc2 -b2c -ac2 -bcd -c3 -b2d -acd -bd2 -c2d a 0|
| ad   0    0    bc  bd   0    0    c2   cd   0    0   cd   d2   0    0    0 a|
| ab   -ac  -ad  ab  b2   -bc  -bd  ac   bc   -c2  -cd ad   bd   -cd  -d2  0 0|
| 0    a2   ab   0   0    ab   b2   0    0    ac   bc  0    0    ad   bd   0 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|ab3-a3c a2c2-ab2d ac3-abd2 b2c-abd b4-a2bc abc2-b3d bc3-b2d2 bc2-acd b3c-a2c2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|--------------------------------------------------------------+              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|--------------------------------------------------------------+              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|--------------------------------------------------------------+              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|--------------------------------------------------------------+              |
| 0 0 b 0 0 0 c 0 0 0 d 0 0 0 |                                |              |
| 0 0 0 b 0 0 0 c 0 0 0 d 0 0 |                                |              |
| a 0 0 0 b 0 0 0 c 0 0 0 d 0 |                                |              |
| 0 a 0 0 0 b 0 0 0 c 0 0 0 d |                                |              |
|                                                              |              |
|                                                              |              |
|--------------------------------------------------------------+              |
| ac3-b2cd c4-bcd2 bcd-ad2 b3d-a2cd ac2d-b2d2 c3d-bd3 a b c d ||              |
|                                                              |              |
|                                                              |              |
|--------------------------------------------------------------+              |
+-----------------------------------------------------------------------------+
|i7 : E_1                                                                     |
|                                                                             |
|     +-----------------------------------------------------------------------|
|o7 = |subquotient (| a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab|
|     |                                                                       |
|     |{-4, 4}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 3}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 2}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 1}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 0}                                                                |
|     +-----------------------------------------------------------------------|
|                                                                             |
|o7 : SpectralSequencePage                                                    |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d3 c4 c3d c2d2 cd3 d4 a4bc-a5d a4b3-a6c a5c2-a4b2d a4c3-a4bd2 a3b2c-a4bd a3b4|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-a5bc a4bc2-a3b3d a3bc3-a3b2d2 a3bc2-a4cd a3b3c-a5c2 a4c3-a3b2cd a3c4-a3bcd2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|a3bcd-a4d2 a3b3d-a5cd a4c2d-a3b2d2 a3c3d-a3bd3 a2b3c-a3b2d a2b5-a4b2c a3b2c2-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|a2b4d a2b2c3-a2b3d2 a2b2c2-a3bcd a2b4c-a4bc2 a3bc3-a2b3cd a2bc4-a2b2cd2 a2b2c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d-a3bd2 a2b4d-a4bcd a3bc2d-a2b3d2 a2bc3d-a2b2d3 a2bc3-a3c2d a2b3c2-a4c3 a3c4-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|a2b2c2d a2c5-a2bc2d2 a2bc2d-a3cd2 a2b3cd-a4c2d a3c3d-a2b2cd2 a2c4d-a2bcd3 a2b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|cd2-a3d3 a2b3d2-a4cd2 a3c2d2-a2b2d3 a2c3d2-a2bd4 ab4c-a2b3d ab6-a3b3c a2b3c2-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|ab5d ab3c3-ab4d2 ab3c2-a2b2cd ab5c-a3b2c2 a2b2c3-ab4cd ab2c4-ab3cd2 ab3cd-a2b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2d2 ab5d-a3b2cd a2b2c2d-ab4d2 ab2c3d-ab3d3 ab2c3-a2bc2d ab4c2-a3bc3 a2bc4-ab3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c2d abc5-ab2c2d2 ab2c2d-a2bcd2 ab4cd-a3bc2d a2bc3d-ab3cd2 abc4d-ab2cd3 ab2cd2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-a2bd3 ab4d2-a3bcd2 a2bc2d2-ab3d3 abc3d2-ab2d4 abc4-a2c3d ab3c3-a3c4 a2c5-ab2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c3d ac6-abc3d2 abc3d-a2c2d2 ab3c2d-a3c3d a2c4d-ab2c2d2 ac5d-abc2d3 abc2d2-a2c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d3 ab3cd2-a3c2d2 a2c3d2-ab2cd3 ac4d2-abcd4 abcd3-a2d4 ab3d3-a3cd3 a2c2d3-ab2d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|4 ac3d3-abd5 b5c-ab4d b7-a2b4c ab4c2-b6d b4c3-b5d2 b4c2-ab3cd b6c-a2b3c2 ab3c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|3-b5cd b3c4-b4cd2 b4cd-ab3d2 b6d-a2b3cd ab3c2d-b5d2 b3c3d-b4d3 b3c3-ab2c2d b5|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c2-a2b2c3 ab2c4-b4c2d b2c5-b3c2d2 b3c2d-ab2cd2 b5cd-a2b2c2d ab2c3d-b4cd2 b2c4|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d-b3cd3 b3cd2-ab2d3 b5d2-a2b2cd2 ab2c2d2-b4d3 b2c3d2-b3d4 b2c4-abc3d b4c3-a2b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c4 abc5-b3c3d bc6-b2c3d2 b2c3d-abc2d2 b4c2d-a2bc3d abc4d-b3c2d2 bc5d-b2c2d3 b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2c2d2-abcd3 b4cd2-a2bc2d2 abc3d2-b3cd3 bc4d2-b2cd4 b2cd3-abd4 b4d3-a2bcd3 abc|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2d3-b3d4 bc3d3-b2d5 bc5-ac4d b3c4-a2c5 ac6-b2c4d c7-bc4d2 bc4d-ac3d2 b3c3d-a2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c4d ac5d-b2c3d2 c6d-bc3d3 bc3d2-ac2d3 b3c2d2-a2c3d2 ac4d2-b2c2d3 c5d2-bc2d4 b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c2d3-acd4 b3cd3-a2c2d3 ac3d3-b2cd4 c4d3-bcd5 bcd4-ad5 b3d4-a2cd4 ac2d4-b2d5 c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|3d4-bd6 0 |, | a4bc-a5d a4b3-a6c a5c2-a4b2d a4c3-a4bd2 a3b2c-a4bd a3b4-a5bc a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|4bc2-a3b3d a3bc3-a3b2d2 a3bc2-a4cd a3b3c-a5c2 a4c3-a3b2cd a3c4-a3bcd2 a3bcd-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|4d2 a3b3d-a5cd a4c2d-a3b2d2 a3c3d-a3bd3 a2b3c-a3b2d a2b5-a4b2c a3b2c2-a2b4d a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2b2c3-a2b3d2 a2b2c2-a3bcd a2b4c-a4bc2 a3bc3-a2b3cd a2bc4-a2b2cd2 a2b2cd-a3bd2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| a2b4d-a4bcd a3bc2d-a2b3d2 a2bc3d-a2b2d3 a2bc3-a3c2d a2b3c2-a4c3 a3c4-a2b2c2d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| a2c5-a2bc2d2 a2bc2d-a3cd2 a2b3cd-a4c2d a3c3d-a2b2cd2 a2c4d-a2bcd3 a2bcd2-a3d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|3 a2b3d2-a4cd2 a3c2d2-a2b2d3 a2c3d2-a2bd4 ab4c-a2b3d ab6-a3b3c a2b3c2-ab5d ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|3c3-ab4d2 ab3c2-a2b2cd ab5c-a3b2c2 a2b2c3-ab4cd ab2c4-ab3cd2 ab3cd-a2b2d2 ab5|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d-a3b2cd a2b2c2d-ab4d2 ab2c3d-ab3d3 ab2c3-a2bc2d ab4c2-a3bc3 a2bc4-ab3c2d abc|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|5-ab2c2d2 ab2c2d-a2bcd2 ab4cd-a3bc2d a2bc3d-ab3cd2 abc4d-ab2cd3 ab2cd2-a2bd3 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|ab4d2-a3bcd2 a2bc2d2-ab3d3 abc3d2-ab2d4 abc4-a2c3d ab3c3-a3c4 a2c5-ab2c3d ac6|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-abc3d2 abc3d-a2c2d2 ab3c2d-a3c3d a2c4d-ab2c2d2 ac5d-abc2d3 abc2d2-a2cd3 ab3c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d2-a3c2d2 a2c3d2-ab2cd3 ac4d2-abcd4 abcd3-a2d4 ab3d3-a3cd3 a2c2d3-ab2d4 ac3d3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-abd5 b5c-ab4d b7-a2b4c ab4c2-b6d b4c3-b5d2 b4c2-ab3cd b6c-a2b3c2 ab3c3-b5cd |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|b3c4-b4cd2 b4cd-ab3d2 b6d-a2b3cd ab3c2d-b5d2 b3c3d-b4d3 b3c3-ab2c2d b5c2-a2b2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c3 ab2c4-b4c2d b2c5-b3c2d2 b3c2d-ab2cd2 b5cd-a2b2c2d ab2c3d-b4cd2 b2c4d-b3cd3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| b3cd2-ab2d3 b5d2-a2b2cd2 ab2c2d2-b4d3 b2c3d2-b3d4 b2c4-abc3d b4c3-a2bc4 abc5|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-b3c3d bc6-b2c3d2 b2c3d-abc2d2 b4c2d-a2bc3d abc4d-b3c2d2 bc5d-b2c2d3 b2c2d2-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|bcd3 b4cd2-a2bc2d2 abc3d2-b3cd3 bc4d2-b2cd4 b2cd3-abd4 b4d3-a2bcd3 abc2d3-b3d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|4 bc3d3-b2d5 bc5-ac4d b3c4-a2c5 ac6-b2c4d c7-bc4d2 bc4d-ac3d2 b3c3d-a2c4d ac5|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d-b2c3d2 c6d-bc3d3 bc3d2-ac2d3 b3c2d2-a2c3d2 ac4d2-b2c2d3 c5d2-bc2d4 bc2d3-ac|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d4 b3cd3-a2c2d3 ac3d3-b2cd4 c4d3-bcd5 bcd4-ad5 b3d4-a2cd4 ac2d4-b2d5 c3d4-bd6|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----+-----------------------------------------------------------------------|
| 0 |)|subquotient ({2} | a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   |
|     |             {3} | 0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d |
|     |             {3} | 0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   |
|     |             {3} | 0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   |
|     |                                                                       |
|     |{-3, 4}                                                                |
|-----+-----------------------------------------------------------------------|
|     |subquotient (| a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3 b2c b2d bc2 bc|
|     |                                                                       |
|     |{-3, 3}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|-----+-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-3, 2}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|-----+-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-3, 1}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|-----+-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-3, 0}                                                                |
|-----+-----------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0|
|0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   a|
|a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0|
|0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d bd2 c3 c2d cd2 d3 a3bc-a4d a3b3-a5c a4c2-a3b2d a3c3-a3bd2 a2b2c-a3bd a2b4-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0 |
|cd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc|
|   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0 |
|   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|4bc a3bc2-a2b3d a2bc3-a2b2d2 a2bc2-a3cd a2b3c-a4c2 a3c3-a2b2cd a2c4-a2bcd2 a2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  0   0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0  |
|2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2|
|  bc2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0  |
|  0   bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bcd-a3d2 a2b3d-a4cd a3c2d-a2b2d2 a2c3d-a2bd3 ab3c-a2b2d ab5-a3b2c a2b2c2-ab4d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   0   d3 0  0  0  -a3b2 -a4c -a3bd -a3c2 -a2b3 -a3bc -a2b2d -a2bc2 -a2b2c |
| 0   0   0  d3 0  0  a3c   a3d  0     0     a2bc  a2bd  0      0      a2c2   |
| cd2 0   0  0  d3 0  a4    a3b  -a3c  -a3d  a3b   a2b2  -a2bc  -a2bd  a3c    |
| 0   cd2 0  0  0  d3 0     0    a4    a3b   0     0     a3b    a2b2   0      |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| ab2c3-ab3d2 ab2c2-a2bcd ab4c-a3bc2 a2bc3-ab3cd abc4-ab2cd2 ab2cd-a2bd2 ab4d-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-a3c2 -a2bcd -a2c3 -a2b2d -a3cd -a2bd2 -a2c2d -ab4 -a2b2c -ab3d -ab2c2 -ab3c |
|a2cd  0      0     a2cd   a2d2  0      0      ab2c ab2d   0     0      abc2  |
|a2bc  -a2c2  -a2cd a3d    a2bd  -a2cd  -a2d2  a2b2 ab3    -ab2c -ab2d  a2bc  |
|0     a3c    a2bc  0      0     a3d    a2bd   0    0      a2b2  ab3    0     |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a3bcd a2bc2d-ab3d2 abc3d-ab2d3 abc3-a2c2d ab3c2-a3c3 a2c4-ab2c2d ac5-abc2d2 a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-a2bc2 -ab2cd -abc3 -ab3d -a2bcd -ab2d2 -abc2d -ab2c2 -a2c3 -abc2d -ac4  -ab2|
|abcd   0      0     abcd  abd2   0      0      ac3    ac2d  0      0     ac2d|
|ab2c   -abc2  -abcd a2bd  ab2d   -abcd  -abd2  a2c2   abc2  -ac3   -ac2d a2cd|
|0      a2bc   ab2c  0     0      a2bd   ab2d   0      0     a2c2   abc2  0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bc2d-a2cd2 ab3cd-a3c2d a2c3d-ab2cd2 ac4d-abcd3 abcd2-a2d3 ab3d2-a3cd2 a2c2d2-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|cd -a2c2d -abcd2 -ac3d -ab2d2 -a2cd2 -abd3 -ac2d2 -b5 -ab3c -b4d -b3c2 -b4c -|
|   acd2   0      0     acd2   ad3    0     0      b3c b3d   0    0     b2c2 b|
|   abcd   -ac2d  -acd2 a2d2   abd2   -acd2 -ad3   ab3 b4    -b3c -b3d  ab2c b|
|   0      a2cd   abcd  0      0      a2d2  abd2   0   0     ab3  b4    0    0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|ab2d3 ac3d2-abd4 b4c-ab3d b6-a2b3c ab3c2-b5d b3c3-b4d2 b3c2-ab2cd b5c-a2b2c2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|ab2c2 -b3cd -b2c3 -b4d -ab2cd -b3d2 -b2c2d -b3c2 -abc3 -b2c2d -bc4  -b3cd -ab|
|2cd   0     0     b2cd b2d2   0     0      bc3   bc2d  0      0     bc2d  bcd|
|3c    -b2c2 -b2cd ab2d b3d    -b2cd -b2d2  abc2  b2c2  -bc3   -bc2d abcd  b2c|
|      ab2c  b3c   0    0      ab2d  b3d    0     0     abc2   b2c2  0     0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|ab2c3-b4cd b2c4-b3cd2 b3cd-ab2d2 b5d-a2b2cd ab2c2d-b4d2 b2c3d-b3d3 b2c3-abc2d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c2d -b2cd2 -bc3d -b3d2 -abcd2 -b2d3 -bc2d2 -b2c3 -ac4 -bc3d -c5  -b2c2d -ac3d|
|2   0      0     bcd2  bd3    0     0      c4    c3d  0     0    c3d    c2d2 |
|d   -bc2d  -bcd2 abd2  b2d2   -bcd2 -bd3   ac3   bc3  -c4   -c3d ac2d   bc2d |
|    abcd   b2cd  0     0      abd2  b2d2   0     0    ac3   bc3  0      0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| b4c2-a2bc3 abc4-b3c2d bc5-b2c2d2 b2c2d-abcd2 b4cd-a2bc2d abc3d-b3cd2 bc4d-b2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| -bc2d2 -c4d  -b2cd2 -ac2d2 -bcd3 -c3d2 -b2d3 -acd3 -bd4 -c2d3 a4 0  0  0  a3|
| 0      0     c2d2   cd3    0     0     cd3   d4    0    0     0  a4 0  0  0 |
| -c3d   -c2d2 acd2   bcd2   -c2d2 -cd3  ad3   bd3   -cd3 -d4   0  0  a4 0  0 |
| ac2d   bc2d  0      0      acd2  bcd2  0     0     ad3  bd3   0  0  0  a4 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|cd3 b2cd2-abd3 b4d2-a2bcd2 abc2d2-b3d3 bc3d2-b2d4 bc4-ac3d b3c3-a2c4 ac5-b2c3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|b 0   0   0   a3c 0   0   0   a3d 0   0   0   a2b2 0    0    0    a2bc 0    0|
|  a3b 0   0   0   a3c 0   0   0   a3d 0   0   0    a2b2 0    0    0    a2bc 0|
|  0   a3b 0   0   0   a3c 0   0   0   a3d 0   0    0    a2b2 0    0    0    a|
|  0   0   a3b 0   0   0   a3c 0   0   0   a3d 0    0    0    a2b2 0    0    0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d c6-bc3d2 bc3d-ac2d2 b3c2d-a2c3d ac4d-b2c2d2 c5d-bc2d3 bc2d2-acd3 b3cd2-a2c2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0  |
|    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d|
|2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0  |
|    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2 ac3d2-b2cd3 c4d2-bcd4 bcd3-ad4 b3d3-a2cd3 ac2d3-b2d4 c3d3-bd5 a4 a3b a3c a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  0    0    ab3 0   0   0   ab2c 0    0    0    ab2d 0    0    0    abc2 0   |
|2 0    0    0   ab3 0   0   0    ab2c 0    0    0    ab2d 0    0    0    abc2|
|  a2d2 0    0   0   ab3 0   0    0    ab2c 0    0    0    ab2d 0    0    0   |
|  0    a2d2 0   0   0   ab3 0    0    0    ab2c 0    0    0    ab2d 0    0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab2d abc2 abcd abd2 ac3 ac2d acd2 a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0    0    abcd 0    0    0    abd2 0    0    0    ac3 0   0   0   ac2d 0    |
| 0    0    0    abcd 0    0    0    abd2 0    0    0   ac3 0   0   0    ac2d |
| abc2 0    0    0    abcd 0    0    0    abd2 0    0   0   ac3 0   0    0    |
| 0    abc2 0    0    0    abcd 0    0    0    abd2 0   0   0   ac3 0    0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 bd3 c4 c3d c2d2 cd3 d4 |, | a3bc-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0    0    acd2 0    0    0    ad3 0   0   0   b4 0  0  0  b3c 0   0   0   b3d|
|0    0    0    acd2 0    0    0   ad3 0   0   0  b4 0  0  0   b3c 0   0   0  |
|ac2d 0    0    0    acd2 0    0   0   ad3 0   0  0  b4 0  0   0   b3c 0   0  |
|0    ac2d 0    0    0    acd2 0   0   0   ad3 0  0  0  b4 0   0   0   b3c 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|4d a3b3-a5c a4c2-a3b2d a3c3-a3bd2 a2b2c-a3bd a2b4-a4bc a3bc2-a2b3d a2bc3-a2b2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   0   0   b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0    bc3 |
| b3d 0   0   0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0   |
| 0   b3d 0   0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0   |
| 0   0   b3d 0    0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2 a2bc2-a3cd a2b3c-a4c2 a3c3-a2b2cd a2c4-a2bcd2 a2bcd-a3d2 a2b3d-a4cd a3c2d-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0   0   0   bc2d 0    0    0    bcd2 0    0    0    bd3 0   0   0   c4 0  0  |
|bc3 0   0   0    bc2d 0    0    0    bcd2 0    0    0   bd3 0   0   0  c4 0  |
|0   bc3 0   0    0    bc2d 0    0    0    bcd2 0    0   0   bd3 0   0  0  c4 |
|0   0   bc3 0    0    0    bc2d 0    0    0    bcd2 0   0   0   bd3 0  0  0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a2b2d2 a2c3d-a2bd3 ab3c-a2b2d ab5-a3b2c a2b2c2-ab4d ab2c3-ab3d2 ab2c2-a2bcd a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0  c3d 0   0   0   c2d2 0    0    0    cd3 0   0   0   d4 0  0  0  |, {2} | -|
|0  0   c3d 0   0   0    c2d2 0    0    0   cd3 0   0   0  d4 0  0  |  {3} | a|
|0  0   0   c3d 0   0    0    c2d2 0    0   0   cd3 0   0  0  d4 0  |  {3} | a|
|c4 0   0   0   c3d 0    0    0    c2d2 0   0   0   cd3 0  0  0  d4 |  {3} | 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b4c-a3bc2 a2bc3-ab3cd abc4-ab2cd2 ab2cd-a2bd2 ab4d-a3bcd a2bc2d-ab3d2 abc3d-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|a3b2 -a4c -a3bd -a3c2 -a2b3 -a3bc -a2b2d -a2bc2 -a2b2c -a3c2 -a2bcd -a2c3 -a2|
|3c   a3d  0     0     a2bc  a2bd  0      0      a2c2   a2cd  0      0     a2c|
|4    a3b  -a3c  -a3d  a3b   a2b2  -a2bc  -a2bd  a3c    a2bc  -a2c2  -a2cd a3d|
|     0    a4    a3b   0     0     a3b    a2b2   0      0     a3c    a2bc  0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b2d3 abc3-a2c2d ab3c2-a3c3 a2c4-ab2c2d ac5-abc2d2 abc2d-a2cd2 ab3cd-a3c2d a2c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|b2d -a3cd -a2bd2 -a2c2d -ab4 -a2b2c -ab3d -ab2c2 -ab3c -a2bc2 -ab2cd -abc3 -a|
|d   a2d2  0      0      ab2c ab2d   0     0      abc2  abcd   0      0     ab|
|    a2bd  -a2cd  -a2d2  a2b2 ab3    -ab2c -ab2d  a2bc  ab2c   -abc2  -abcd a2|
|    0     a3d    a2bd   0    0      a2b2  ab3    0     0      a2bc   ab2c  0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3d-ab2cd2 ac4d-abcd3 abcd2-a2d3 ab3d2-a3cd2 a2c2d2-ab2d3 ac3d2-abd4 b4c-ab3d |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|b3d -a2bcd -ab2d2 -abc2d -ab2c2 -a2c3 -abc2d -ac4  -ab2cd -a2c2d -abcd2 -ac3d|
|cd  abd2   0      0      ac3    ac2d  0      0     ac2d   acd2   0      0    |
|bd  ab2d   -abcd  -abd2  a2c2   abc2  -ac3   -ac2d a2cd   abcd   -ac2d  -acd2|
|    0      a2bd   ab2d   0      0     a2c2   abc2  0      0      a2cd   abcd |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b6-a2b3c ab3c2-b5d b3c3-b4d2 b3c2-ab2cd b5c-a2b2c2 ab2c3-b4cd b2c4-b3cd2 b3cd|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| -ab2d2 -a2cd2 -abd3 -ac2d2 -b5 -ab3c -b4d -b3c2 -b4c -ab2c2 -b3cd -b2c3 -b4d|
| acd2   ad3    0     0      b3c b3d   0    0     b2c2 b2cd   0     0     b2cd|
| a2d2   abd2   -acd2 -ad3   ab3 b4    -b3c -b3d  ab2c b3c    -b2c2 -b2cd ab2d|
| 0      0      a2d2  abd2   0   0     ab3  b4    0    0      ab2c  b3c   0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-ab2d2 b5d-a2b2cd ab2c2d-b4d2 b2c3d-b3d3 b2c3-abc2d b4c2-a2bc3 abc4-b3c2d bc5|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| -ab2cd -b3d2 -b2c2d -b3c2 -abc3 -b2c2d -bc4  -b3cd -abc2d -b2cd2 -bc3d -b3d2|
| b2d2   0     0      bc3   bc2d  0      0     bc2d  bcd2   0      0     bcd2 |
| b3d    -b2cd -b2d2  abc2  b2c2  -bc3   -bc2d abcd  b2cd   -bc2d  -bcd2 abd2 |
| 0      ab2d  b3d    0     0     abc2   b2c2  0     0      abcd   b2cd  0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-b2c2d2 b2c2d-abcd2 b4cd-a2bc2d abc3d-b3cd2 bc4d-b2cd3 b2cd2-abd3 b4d2-a2bcd2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| -abcd2 -b2d3 -bc2d2 -b2c3 -ac4 -bc3d -c5  -b2c2d -ac3d -bc2d2 -c4d  -b2cd2 -|
| bd3    0     0      c4    c3d  0     0    c3d    c2d2  0      0     c2d2   c|
| b2d2   -bcd2 -bd3   ac3   bc3  -c4   -c3d ac2d   bc2d  -c3d   -c2d2 acd2   b|
| 0      abd2  b2d2   0     0    ac3   bc3  0      0     ac2d   bc2d  0      0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| abc2d2-b3d3 bc3d2-b2d4 bc4-ac3d b3c3-a2c4 ac5-b2c3d c6-bc3d2 bc3d-ac2d2 b3c2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|ac2d2 -bcd3 -c3d2 -b2d3 -acd3 -bd4 -c2d3 a4 0  0  0  a3b 0   0   0   a3c 0   |
|d3    0     0     cd3   d4    0    0     0  a4 0  0  0   a3b 0   0   0   a3c |
|cd2   -c2d2 -cd3  ad3   bd3   -cd3 -d4   0  0  a4 0  0   0   a3b 0   0   0   |
|      acd2  bcd2  0     0     ad3  bd3   0  0  0  a4 0   0   0   a3b 0   0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d-a2c3d ac4d-b2c2d2 c5d-bc2d3 bc2d2-acd3 b3cd2-a2c2d2 ac3d2-b2cd3 c4d2-bcd4 b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0   0   a3d 0   0   0   a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0  |
|0   0   0   a3d 0   0   0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0  |
|a3c 0   0   0   a3d 0   0    0    a2b2 0    0    0    a2bc 0    0    0    a2b|
|0   a3c 0   0   0   a3d 0    0    0    a2b2 0    0    0    a2bc 0    0    0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|cd3-ad4 b3d3-a2cd3 ac2d3-b2d4 c3d3-bd5 a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0    0    ab3 0   0 |
|  0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0    0   ab3 0 |
|d 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0   0   ab|
|  a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0   0   0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d a2d2 ab3 ab2c ab2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  0   ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0|
|  0   0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0|
|3 0   0    0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    a|
|  ab3 0    0    0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2 bc3 bc2d bcd2 bd3 c4 c3d c2d2 cd3 d4 |)                                   |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|    0    abd2 0    0    0    ac3 0   0   0   ac2d 0    0    0    acd2 0    0 |
|    0    0    abd2 0    0    0   ac3 0   0   0    ac2d 0    0    0    acd2 0 |
|bcd 0    0    0    abd2 0    0   0   ac3 0   0    0    ac2d 0    0    0    ac|
|    abcd 0    0    0    abd2 0   0   0   ac3 0    0    0    ac2d 0    0    0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|   0    ad3 0   0   0   b4 0  0  0  b3c 0   0   0   b3d 0   0   0   b2c2 0   |
|   0    0   ad3 0   0   0  b4 0  0  0   b3c 0   0   0   b3d 0   0   0    b2c2|
|d2 0    0   0   ad3 0   0  0  b4 0  0   0   b3c 0   0   0   b3d 0   0    0   |
|   acd2 0   0   0   ad3 0  0  0  b4 0   0   0   b3c 0   0   0   b3d 0    0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0    0    b2cd 0    0    0    b2d2 0    0    0    bc3 0   0   0   bc2d 0    |
| 0    0    0    b2cd 0    0    0    b2d2 0    0    0   bc3 0   0   0    bc2d |
| b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0   0   bc3 0   0    0    |
| 0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0   0   0   bc3 0    0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0    0    bcd2 0    0    0    bd3 0   0   0   c4 0  0  0  c3d 0   0   0   c2d|
|0    0    0    bcd2 0    0    0   bd3 0   0   0  c4 0  0  0   c3d 0   0   0  |
|bc2d 0    0    0    bcd2 0    0   0   bd3 0   0  0  c4 0  0   0   c3d 0   0  |
|0    bc2d 0    0    0    bcd2 0   0   0   bd3 0  0  0  c4 0   0   0   c3d 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------+-----------------------------|
|2 0    0    0    cd3 0   0   0   d4 0  0  0  |)|subquotient ({4} | a2 0  0  0|
|  c2d2 0    0    0   cd3 0   0   0  d4 0  0  | |             {4} | 0  a2 0  0|
|  0    c2d2 0    0   0   cd3 0   0  0  d4 0  | |             {4} | 0  0  a2 0|
|  0    0    c2d2 0   0   0   cd3 0  0  0  d4 | |             {4} | 0  0  0  a|
|                                               |                             |
|                                               |{-2, 4}                      |
|-----------------------------------------------+-----------------------------|
|                                               |subquotient ({2} | a2 0  0  0|
|                                               |             {3} | 0  a2 0  0|
|                                               |             {3} | 0  0  a2 0|
|                                               |             {3} | 0  0  0  a|
|                                               |                             |
|                                               |{-2, 3}                      |
|-----------------------------------------------+-----------------------------|
|                                               |subquotient (| a2 ab ac ad b2|
|                                               |                             |
|                                               |{-2, 2}                      |
|                                               |                             |
|                                               |                             |
|                                               |                             |
|-----------------------------------------------+-----------------------------|
|                                               |0                            |
|                                               |                             |
|                                               |{-2, 1}                      |
|                                               |                             |
|                                               |                             |
|                                               |                             |
|-----------------------------------------------+-----------------------------|
|                                               |0                            |
|                                               |                             |
|                                               |{-2, 0}                      |
|-----------------------------------------------+-----------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 |
|  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  |
|  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  |
|2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 |
|  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  |
|  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  |
|2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| bc bd c2 cd d2 a2bc-a3d a2b3-a4c a3c2-a2b2d a2c3-a2bd2 ab2c-a2bd ab4-a3bc a2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0  0  0  cd 0  0  0  d2 0  0  0  a2d  abd  acd  ad2  b2d  bcd  bd2  c2d  cd2 |
|c2 0  0  0  cd 0  0  0  d2 0  0  -a2c -abc -ac2 -acd -b2c -bc2 -bcd -c3  -c2d|
|0  c2 0  0  0  cd 0  0  0  d2 0  -a2b -ab2 -abc -abd -b3  -b2c -b2d -bc2 -bcd|
|0  0  c2 0  0  0  cd 0  0  0  d2 a3   a2b  a2c  a2d  ab2  abc  abd  ac2  acd |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|0  0  0  cd 0  0  0  d2 0  0  0  -a2b2 -a3c -a2bd -a2c2 -ab3 -a2bc -ab2d -abc|
|c2 0  0  0  cd 0  0  0  d2 0  0  a2c   a2d  0     0     abc  abd   0     0   |
|0  c2 0  0  0  cd 0  0  0  d2 0  a3    a2b  -a2c  -a2d  a2b  ab2   -abc  -abd|
|0  0  c2 0  0  0  cd 0  0  0  d2 0     0    a3    a2b   0    0     a2b   ab2 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bc2-ab3d abc3-ab2d2 abc2-a2cd ab3c-a3c2 a2c3-ab2cd ac4-abcd2 abcd-a2d2 ab3d-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| d3   a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0  |
| -cd2 0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0  |
| -bd2 0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2|
| ad2  0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2 -ab2c -a2c2 -abcd -ac3 -ab2d -a2cd -abd2 -ac2d -b4 -ab2c -b3d -b2c2 -b3c -a|
|  ac2   acd   0     0    acd   ad2   0     0     b2c b2d   0    0     bc2  bc|
|  a2c   abc   -ac2  -acd a2d   abd   -acd  -ad2  ab2 b3    -b2c -b2d  abc  b2|
|  0     0     a2c   abc  0     0     a2d   abd   0   0     ab2  b3    0    0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3cd a2c2d-ab2d2 ac3d-abd3 b3c-ab2d b5-a2b2c ab2c2-b4d b2c3-b3d2 b2c2-abcd b4c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   |
| 0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 |
| 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   |
| ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bc2 -b2cd -bc3 -b3d -abcd -b2d2 -bc2d -b2c2 -ac3 -bc2d -c4  -b2cd -ac2d -bcd2|
|d   0     0    bcd  bd2   0     0     c3    c2d  0     0    c2d   cd2   0    |
|c   -bc2  -bcd abd  b2d   -bcd  -bd2  ac2   bc2  -c3   -c2d acd   bcd   -c2d |
|    abc   b2c  0    0     abd   b2d   0     0    ac2   bc2  0     0     acd  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-a2bc2 abc3-b3cd bc4-b2cd2 b2cd-abd2 b4d-a2bcd abc2d-b3d2 bc3d-b2d3 bc3-ac2d |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0|
|0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0|
|ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   b|
|0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| -c3d -b2d2 -acd2 -bd3 -c2d2 a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d |
| 0    cd2   d3    0    0     0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   |
| -cd2 ad2   bd2   -cd2 -d3   0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   |
| bcd  0     0     ad2  bd2   0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b3c2-a2c3 ac4-b2c2d c5-bc2d2 bc2d-acd2 b3cd-a2c2d ac3d-b2cd2 c4d-bcd3 bcd2-ad|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0   0   d3 0  0  0|
|   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0   0   0  d3 0  0|
|cd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2 0   0  0  d3 0|
|   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0   cd2 0  0  0  d|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   a|
|a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0|
|0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0|
|0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3 b3d2-a2cd2 ac2d2-b2d3 c3d2-bd4 a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3 b2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  |, {4} | a2d  abd  acd  ad2  b2d  bcd  bd2  c2d  cd2  d3   a3 0  0  0  a2b |
|  |  {4} | -a2c -abc -ac2 -acd -b2c -bc2 -bcd -c3  -c2d -cd2 0  a3 0  0  0   |
|  |  {4} | -a2b -ab2 -abc -abd -b3  -b2c -b2d -bc2 -bcd -bd2 0  0  a3 0  0   |
|3 |  {4} | a3   a2b  a2c  a2d  ab2  abc  abd  ac2  acd  ad2  0  0  0  a3 0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|cd 0   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc|
|   acd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0 |
|   0   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0 |
|   0   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c b2d bc2 bcd bd2 c3 c2d cd2 d3 |, | a2bc-a3d a2b3-a4c a3c2-a2b2d a2c3-a2bd2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   a|
|a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0|
|0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0|
|0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2 0   0   0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2|
|  bc2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0  |
|  0   bc2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0  |
|  0   0   bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|ab2c-a2bd ab4-a3bc a2bc2-ab3d abc3-ab2d2 abc2-a2cd ab3c-a3c2 a2c3-ab2cd ac4-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|bd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0   b3 0  0  0  b2|
|   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0  b3 0  0  0 |
|   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0  0  b3 0  0 |
|   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0  0  0  b3 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0   0   0   d3 0  0  0  |, {2} | -a2b2 -a3c -a2bd -a2c2 -ab3 -a2bc -ab2d -ab|
| cd2 0   0   0  d3 0  0  |  {3} | a2c   a2d  0     0     abc  abd   0     0  |
| 0   cd2 0   0  0  d3 0  |  {3} | a3    a2b  -a2c  -a2d  a2b  ab2   -abc  -ab|
| 0   0   cd2 0  0  0  d3 |  {3} | 0     0    a3    a2b   0    0     a2b   ab2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bcd2 abcd-a2d2 ab3d-a3cd a2c2d-ab2d2 ac3d-abd3 b3c-ab2d b5-a2b2c ab2c2-b4d b2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0  |
|  b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0  |
|  0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0  |
|  0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2 -ab2c -a2c2 -abcd -ac3 -ab2d -a2cd -abd2 -ac2d -b4 -ab2c -b3d -b2c2 -b3c -|
|   ac2   acd   0     0    acd   ad2   0     0     b2c b2d   0    0     bc2  b|
|d  a2c   abc   -ac2  -acd a2d   abd   -acd  -ad2  ab2 b3    -b2c -b2d  abc  b|
|   0     0     a2c   abc  0     0     a2d   abd   0   0     ab2  b3    0    0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c3-b3d2 b2c2-abcd b4c-a2bc2 abc3-b3cd bc4-b2cd2 b2cd-abd2 b4d-a2bcd abc2d-b3d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| c3 0  0  0  c2d 0   0   0   cd2 0   0   0   d3 0  0  0  |)                  |
| 0  c3 0  0  0   c2d 0   0   0   cd2 0   0   0  d3 0  0  |                   |
| 0  0  c3 0  0   0   c2d 0   0   0   cd2 0   0  0  d3 0  |                   |
| 0  0  0  c3 0   0   0   c2d 0   0   0   cd2 0  0  0  d3 |                   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|abc2 -b2cd -bc3 -b3d -abcd -b2d2 -bc2d -b2c2 -ac3 -bc2d -c4  -b2cd -ac2d -bcd|
|cd   0     0    bcd  bd2   0     0     c3    c2d  0     0    c2d   cd2   0   |
|2c   -bc2  -bcd abd  b2d   -bcd  -bd2  ac2   bc2  -c3   -c2d acd   bcd   -c2d|
|     abc   b2c  0    0     abd   b2d   0     0    ac2   bc2  0     0     acd |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2 bc3d-b2d3 bc3-ac2d b3c2-a2c3 ac4-b2c2d c5-bc2d2 bc2d-acd2 b3cd-a2c2d ac3d-b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2 -c3d -b2d2 -acd2 -bd3 -c2d2 a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d|
|  0    cd2   d3    0    0     0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0  |
|  -cd2 ad2   bd2   -cd2 -d3   0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0  |
|  bcd  0     0     ad2  bd2   0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2cd2 c4d-bcd3 bcd2-ad3 b3d2-a2cd2 ac2d2-b2d3 c3d2-bd4 a3 a2b a2c a2d ab2 abc |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   |
| a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   |
| 0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   |
| 0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|abd ac2 acd ad2 b3 b2c b2d bc2 bcd bd2 c3 c2d cd2 d3 |)                      |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|acd 0   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   b|
|0   acd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0|
|0   0   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0|
|0   0   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2 0   0   0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd|
|   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0 |
|   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0 |
|   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|----------------------------+------------------------------------------------|
|                            |subquotient ({5} | a b c d a2 ab ac ad b2 bc bd |
|                            |                                                |
|                            |{-1, 4}                                         |
|                            |                                                |
|                            |                                                |
|                            |                                                |
|----------------------------+------------------------------------------------|
|2 0   0   0   d3 0  0  0  |)|subquotient ({4} | a 0 0 0 b 0 0 0 c 0 0 0 d 0 0|
|  cd2 0   0   0  d3 0  0  | |             {4} | 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0|
|  0   cd2 0   0  0  d3 0  | |             {4} | 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d|
|  0   0   cd2 0  0  0  d3 | |             {4} | 0 0 0 a 0 0 0 b 0 0 0 c 0 0 0|
|                            |                                                |
|                            |{-1, 3}                                         |
|----------------------------+------------------------------------------------|
|                            |subquotient ({2} | a 0 0 0 b 0 0 0 c 0 0 0 d 0 0|
|                            |             {3} | 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0|
|                            |             {3} | 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d|
|                            |             {3} | 0 0 0 a 0 0 0 b 0 0 0 c 0 0 0|
|                            |                                                |
|                            |{-1, 2}                                         |
|----------------------------+------------------------------------------------|
|                            |subquotient (| a b c d abc-a2d ab3-a3c a2c2-ab2d|
|                            |                                                |
|                            |{-1, 1}                                         |
|                            |                                                |
|                            |                                                |
|                            |                                                |
|----------------------------+------------------------------------------------|
|                            |0                                               |
|                            |                                                |
|                            |{-1, 0}                                         |
|----------------------------+------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c2 cd d2 |, {5} | a2 ab ac ad b2 bc bd c2 cd d2 |)                           |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0 ad  bd  cd  d2  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0|
| 0 -ac -bc -c2 -cd 0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0|
| 0 -ab -b2 -bc -bd 0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0|
| d a2  ab  ac  ad  0  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0 -ab2 -a2c -abd -ac2 -b3 -abc -b2d -bc2 -b2c -ac2 -bcd -c3 -b2d -acd -bd2 -|
| 0 ac   ad   0    0    bc  bd   0    0    c2   cd   0    0   cd   d2   0    0|
| 0 a2   ab   -ac  -ad  ab  b2   -bc  -bd  ac   bc   -c2  -cd ad   bd   -cd  -|
| d 0    0    a2   ab   0   0    ab   b2   0    0    ac   bc  0    0    ad   b|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| ac3-abd2 b2c-abd b4-a2bc abc2-b3d bc3-b2d2 bc2-acd b3c-a2c2 ac3-b2cd c4-bcd2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |, {4} | ad  bd|
|  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |  {4} | -ac -b|
|  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |  {4} | -ab -b|
|2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |  {4} | a2  ab|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2d a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  b|
|    0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0|
|d2  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0|
|d   0  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| bcd-ad2 b3d-a2cd ac2d-b2d2 c3d-bd3 a2 ab ac ad b2 bc bd c2 cd d2 |, | abc-a2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  cd  d2  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0|
|c -c2 -cd 0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0|
|2 -bc -bd 0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  b|
|  ac  ad  0  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |, {2} | -ab2 -a2c -abd -ac2 -|
|  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |  {3} | ac   ad   0    0    b|
|  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |  {3} | a2   ab   -ac  -ad  a|
|  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |  {3} | 0    0    a2   ab   0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d ab3-a3c a2c2-ab2d ac3-abd2 b2c-abd b4-a2bc abc2-b3d bc3-b2d2 bc2-acd b3c-a2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |)                      |
|  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |                       |
|c 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |                       |
|  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |                       |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b3 -abc -b2d -bc2 -b2c -ac2 -bcd -c3 -b2d -acd -bd2 -c2d a2 0  0  0  ab 0  0 |
|c  bd   0    0    c2   cd   0    0   cd   d2   0    0    0  a2 0  0  0  ab 0 |
|b  b2   -bc  -bd  ac   bc   -c2  -cd ad   bd   -cd  -d2  0  0  a2 0  0  0  ab|
|   0    ab   b2   0    0    ac   bc  0    0    ad   bd   0  0  0  a2 0  0  0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2 ac3-b2cd c4-bcd2 bcd-ad2 b3d-a2cd ac2d-b2d2 c3d-bd3 a2 ab ac ad b2 bc bd c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  c|
| 0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0|
| 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0|
| ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2 cd d2 |)                                                                   |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-------------------------+---------------------------------------------------|
|                         |0                                                  |
|                         |                                                   |
|                         |{0, 4}                                             |
|                         |                                                   |
|                         |                                                   |
|                         |                                                   |
|-------------------------+---------------------------------------------------|
|                         |cokernel {5} | a b c d |                           |
|                         |                                                   |
|                         |{0, 3}                                             |
|                         |                                                   |
|                         |                                                   |
|                         |                                                   |
|-------------------------+---------------------------------------------------|
|d 0  0  0  d2 0  0  0  |)|cokernel {4} | d  a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 ||
|  cd 0  0  0  d2 0  0  | |         {4} | -c 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 ||
|  0  cd 0  0  0  d2 0  | |         {4} | -b 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 ||
|  0  0  cd 0  0  0  d2 | |         {4} | a  0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d ||
|                         |                                                   |
|                         |{0, 2}                                             |
|-------------------------+---------------------------------------------------|
|                         |cokernel {2} | -b2 -ac -bd -c2 a 0 0 0 b 0 0 0 c 0 |
|                         |         {3} | c   d   0   0   0 a 0 0 0 b 0 0 0 c |
|                         |         {3} | a   b   -c  -d  0 0 a 0 0 0 b 0 0 0 |
|                         |         {3} | 0   0   a   b   0 0 0 a 0 0 0 b 0 0 |
|                         |                                                   |
|                         |{0, 1}                                             |
|-------------------------+---------------------------------------------------|
|                         |cokernel | bc-ad b3-a2c ac2-b2d c3-bd2 a b c d |   |
|                         |                                                   |
|                         |{0, 0}                                             |
|-------------------------+---------------------------------------------------|
|-----------------------------------------------------------------------------|
|-------------+                                                               |
|             |                                                               |
|             |                                                               |
|             |                                                               |
|             |                                                               |
|             |                                                               |
|             |                                                               |
|-------------+                                                               |
|             |                                                               |
|             |                                                               |
|             |                                                               |
|             |                                                               |
|             |                                                               |
|             |                                                               |
|-------------+                                                               |
|             |                                                               |
|             |                                                               |
|             |                                                               |
|             |                                                               |
|             |                                                               |
|             |                                                               |
|-------------+                                                               |
|0 0 d 0 0 0 ||                                                               |
|0 0 0 d 0 0 ||                                                               |
|c 0 0 0 d 0 ||                                                               |
|0 c 0 0 0 d ||                                                               |
|             |                                                               |
|             |                                                               |
|-------------+                                                               |
|             |                                                               |
|             |                                                               |
|             |                                                               |
|-------------+                                                               |
+-----------------------------------------------------------------------------+
|i8 : E_infinity                                                              |
|                                                                             |
|     +-----------------------------------------------------------------------|
|o8 = |subquotient (| a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab|
|     |                                                                       |
|     |{-4, 4}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 3}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 2}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 1}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 0}                                                                |
|     +-----------------------------------------------------------------------|
|                                                                             |
|o8 : Page                                                                    |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d3 c4 c3d c2d2 cd3 d4 bc-ad b3-a2c ac2-b2d c3-bd2 0 |, | bc-ad b3-a2c ac2-b2d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|------------+----------------------------------------------------------------|
| c3-bd2 0 |)|subquotient ({2} | 0 a2b2 a2bd a2bd 0 a3c  a3c  a2c2 a2b2 ab3  a|
|            |             {3} | 0 -a2c 0    0    0 -a2d -a2d 0    -a2c -abc 0|
|            |             {3} | 0 -a3  a2c  a2c  0 -a2b -a2b a2d  -a3  -a2b a|
|            |             {3} | 0 0    -a3  -a3  0 0    0    -a2b 0    0    -|
|            |                                                                |
|            |{-3, 4}                                                         |
|------------+----------------------------------------------------------------|
|            |subquotient (| a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3 b2c b2d|
|            |                                                                |
|            |{-3, 3}                                                         |
|            |                                                                |
|            |                                                                |
|            |                                                                |
|------------+----------------------------------------------------------------|
|            |0                                                               |
|            |                                                                |
|            |{-3, 2}                                                         |
|            |                                                                |
|            |                                                                |
|            |                                                                |
|------------+----------------------------------------------------------------|
|            |0                                                               |
|            |                                                                |
|            |{-3, 1}                                                         |
|            |                                                                |
|            |                                                                |
|            |                                                                |
|------------+----------------------------------------------------------------|
|            |0                                                               |
|            |                                                                |
|            |{-3, 0}                                                         |
|------------+----------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|b2d ab2d a2bd a2bc a2bc a2bc abc2 abc2 a2c2 ab2c ab2c abcd abcd abcd 0       |
|    0    0    -abd -abd -abd 0    0    0    -ac2 -ac2 0    0    0    acd     |
|bc  abc  a2c  -ab2 -ab2 -ab2 abd  abd  a2d  -a2c -a2c ac2  ac2  ac2  abc+a2d |
|a2b -a2b -a3  0    0    0    -ab2 -ab2 -a2b 0    0    -a2c -a2c -a2c -a2b    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| bc2 bcd bd2 c3 c2d cd2 d3 bc-ad b3-a2c ac2-b2d c3-bd2 a4 a3b a3c a3d a2b2 a2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|abd2 ac3  abd2 0 a2cd a2cd a2cd ac2d ac2d ab3  ab2c b4   b3d  b3d  ab2d 0    |
|0    0    0    0 -ad2 -ad2 -ad2 0    0    -abc -ac2 -b2c 0    0    0    -ac2+|
|acd  acd  acd  0 -abd -abd -abd ad2  ad2  -a2b -a2c -ab2 b2c  b2c  abc  b3-a2|
|-a2d -abc -a2d 0 0    0    0    -abd -abd 0    0    0    -ab2 -ab2 -a2b 0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|    b2c2 b2c2 abc2 b3c  b3c  b2cd b2cd b2cd abcd 0       b2d2 bc3  b2d2 abd2 |
|b2d 0    0    0    -bc2 -bc2 0    0    0    0    bcd     0    0    0    0    |
|c   b2d  b2d  abd  -abc -abc bc2  bc2  bc2  ac2  b2c+abd bcd  bcd  bcd  acd  |
|    -b3  -b3  -ab2 0    0    -abc -abc -abc -a2c -ab2    -abd -b2c -abd -a2d |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 bd3 c4 c3d c2d2 cd3 d4 |, | bc-ad b3-a2c ac2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0       bc2d bc2d bc3  ac3  0       0        bc2d ac2d 0       bcd2 bcd2 c4  |
|bd2     0    0    0    0    c3      0        0    0    c2d     0    0    0   |
|ac2+b2d bd2  bd2  bcd  acd  ac2+b2d c3-bd2   bd2  ad2  bc2+acd c2d  c2d  c2d |
|-a2c    -b2d -b2d -b2c -abc -b3     -ac2+b2d -b2d -abd -abc    -acd -acd -bc2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-b2d c3-bd2 a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab2d abc2 a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| bcd2 0       bd3  c3d  c3d  0 bd3  0 acd2 acd2 acd2 c2d2 c2d2 0 0 0         |
| 0    cd2     0    0    0    0 0    0 -d3  -d3  -d3  0    0    0 0 -a2cd     |
| c2d  bcd+ad2 cd2  cd2  cd2  0 cd2  0 -bd2 -bd2 -bd2 d3   d3   0 0 -a2bc-a3d |
| -acd -abd    -ad2 -bcd -bcd 0 -ad2 0 0    0    0    -bd2 -bd2 0 0 a3b       |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 bd3 c4 c3d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0         0 0 0 0 0 0 0 0 0 0 0 0 0 0          0 0          0          0 0 0 |
|-a2cd     0 0 0 0 0 0 0 0 0 0 0 0 0 -a2c2+ab2d 0 -abcd      -abcd      0 0 0 |
|-a2bc-a3d 0 0 0 0 0 0 0 0 0 0 0 0 0 ab3-a3c    0 -ab2c-a2bd -ab2c-a2bd 0 0 0 |
|a3b       0 0 0 0 0 0 0 0 0 0 0 0 0 0          0 a2b2       a2b2       0 0 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| c2d2 cd3 d4 |)                                                              |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0 0 0 0         0 0 0 0 0 0 0 0 0 0         0          0         0           |
|0 0 0 -ac3+abd2 0 0 0 0 0 0 0 0 0 -abc2+b3d -a2c2+ab2d -ac3+abd2 -ac3+b2cd+ab|
|0 0 0 0         0 0 0 0 0 0 0 0 0 b4-a2bc   ab3-a3c    0         b3c+ab2d    |
|0 0 0 ab3-a3c   0 0 0 0 0 0 0 0 0 0         0          ab3-a3c   -a3c        |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|   0 0 0 0 0 0         0 0 0 0 0 0 0 0 0 0 0 0 0 0 -b2 -ac -bd -c2 a4 0  0  0|
|d2 0 0 0 0 0 -bc3+ac2d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c   d   0   0   0  a4 0  0|
|   0 0 0 0 0 -b3d+a2cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a   b   -c  -d  0  0  a4 0|
|   0 0 0 0 0 b4-a2bc   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0   0   a   b   0  0  0  a|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  a3b 0   0   0   a3c 0   0   0   a3d 0   0   0   a2b2 0    0    0    a2bc 0 |
|  0   a3b 0   0   0   a3c 0   0   0   a3d 0   0   0    a2b2 0    0    0    a2|
|  0   0   a3b 0   0   0   a3c 0   0   0   a3d 0   0    0    a2b2 0    0    0 |
|4 0   0   0   a3b 0   0   0   a3c 0   0   0   a3d 0    0    0    a2b2 0    0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|   0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2|
|bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0   |
|   a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0   |
|   0    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0    0    0    ab3 0   0   0   ab2c 0    0    0    ab2d 0    0    0    abc2 |
| a2d2 0    0    0   ab3 0   0   0    ab2c 0    0    0    ab2d 0    0    0    |
| 0    a2d2 0    0   0   ab3 0   0    0    ab2c 0    0    0    ab2d 0    0    |
| 0    0    a2d2 0   0   0   ab3 0    0    0    ab2c 0    0    0    ab2d 0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0    0    0    abcd 0    0    0    abd2 0    0    0    ac3 0   0   0   ac2d 0|
|abc2 0    0    0    abcd 0    0    0    abd2 0    0    0   ac3 0   0   0    a|
|0    abc2 0    0    0    abcd 0    0    0    abd2 0    0   0   ac3 0   0    0|
|0    0    abc2 0    0    0    abcd 0    0    0    abd2 0   0   0   ac3 0    0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|    0    0    acd2 0    0    0    ad3 0   0   0   b4 0  0  0  b3c 0   0   0  |
|c2d 0    0    0    acd2 0    0    0   ad3 0   0   0  b4 0  0  0   b3c 0   0  |
|    ac2d 0    0    0    acd2 0    0   0   ad3 0   0  0  b4 0  0   0   b3c 0  |
|    0    ac2d 0    0    0    acd2 0   0   0   ad3 0  0  0  b4 0   0   0   b3c|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| b3d 0   0   0   b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0    |
| 0   b3d 0   0   0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    |
| 0   0   b3d 0   0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    |
| 0   0   0   b3d 0    0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|bc3 0   0   0   bc2d 0    0    0    bcd2 0    0    0    bd3 0   0   0   c4 0 |
|0   bc3 0   0   0    bc2d 0    0    0    bcd2 0    0    0   bd3 0   0   0  c4|
|0   0   bc3 0   0    0    bc2d 0    0    0    bcd2 0    0   0   bd3 0   0  0 |
|0   0   0   bc3 0    0    0    bc2d 0    0    0    bcd2 0   0   0   bd3 0  0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0  0  c3d 0   0   0   c2d2 0    0    0    cd3 0   0   0   d4 0  0  0  |, {2}|
| 0  0  0   c3d 0   0   0    c2d2 0    0    0   cd3 0   0   0  d4 0  0  |  {3}|
| c4 0  0   0   c3d 0   0    0    c2d2 0    0   0   cd3 0   0  0  d4 0  |  {3}|
| 0  c4 0   0   0   c3d 0    0    0    c2d2 0   0   0   cd3 0  0  0  d4 |  {3}|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| | -b2 -ac -bd -c2 a4 0  0  0  a3b 0   0   0   a3c 0   0   0   a3d 0   0   0 |
| | c   d   0   0   0  a4 0  0  0   a3b 0   0   0   a3c 0   0   0   a3d 0   0 |
| | a   b   -c  -d  0  0  a4 0  0   0   a3b 0   0   0   a3c 0   0   0   a3d 0 |
| | 0   0   a   b   0  0  0  a4 0   0   0   a3b 0   0   0   a3c 0   0   0   a3|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    |
|  0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    |
|  0    0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    a2c2 |
|d 0    0    0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0    a2cd 0    0    0    a2d2 0    0    0    ab3 0   0   0   ab2c 0    0    0|
|0    0    a2cd 0    0    0    a2d2 0    0    0   ab3 0   0   0    ab2c 0    0|
|0    0    0    a2cd 0    0    0    a2d2 0    0   0   ab3 0   0    0    ab2c 0|
|a2c2 0    0    0    a2cd 0    0    0    a2d2 0   0   0   ab3 0    0    0    a|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0    abd2 0    0  |
|    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0    abd2 0  |
|    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0    abd|
|b2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  0    ac3 0   0   0   ac2d 0    0    0    acd2 0    0    0    ad3 0   0   0 |
|  0    0   ac3 0   0   0    ac2d 0    0    0    acd2 0    0    0   ad3 0   0 |
|2 0    0   0   ac3 0   0    0    ac2d 0    0    0    acd2 0    0   0   ad3 0 |
|  abd2 0   0   0   ac3 0    0    0    ac2d 0    0    0    acd2 0   0   0   ad|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  b4 0  0  0  b3c 0   0   0   b3d 0   0   0   b2c2 0    0    0    b2cd 0    0|
|  0  b4 0  0  0   b3c 0   0   0   b3d 0   0   0    b2c2 0    0    0    b2cd 0|
|  0  0  b4 0  0   0   b3c 0   0   0   b3d 0   0    0    b2c2 0    0    0    b|
|3 0  0  0  b4 0   0   0   b3c 0   0   0   b3d 0    0    0    b2c2 0    0    0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|    0    b2d2 0    0    0    bc3 0   0   0   bc2d 0    0    0    bcd2 0    0 |
|    0    0    b2d2 0    0    0   bc3 0   0   0    bc2d 0    0    0    bcd2 0 |
|2cd 0    0    0    b2d2 0    0   0   bc3 0   0    0    bc2d 0    0    0    bc|
|    b2cd 0    0    0    b2d2 0   0   0   bc3 0    0    0    bc2d 0    0    0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|   0    bd3 0   0   0   c4 0  0  0  c3d 0   0   0   c2d2 0    0    0    cd3 0|
|   0    0   bd3 0   0   0  c4 0  0  0   c3d 0   0   0    c2d2 0    0    0   c|
|d2 0    0   0   bd3 0   0  0  c4 0  0   0   c3d 0   0    0    c2d2 0    0   0|
|   bcd2 0   0   0   bd3 0  0  0  c4 0   0   0   c3d 0    0    0    c2d2 0   0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-------------------------+---------------------------------------------------|
|   0   0   d4 0  0  0  |)|subquotient ({4} | ad  bd  cd  d2  a2d  0 0 -abd 0 |
|d3 0   0   0  d4 0  0  | |             {4} | -ac -bc -c2 -cd -a2c 0 0 abc  0 |
|   cd3 0   0  0  d4 0  | |             {4} | -ab -b2 -bc -bd -a2b 0 0 ab2  0 |
|   0   cd3 0  0  0  d4 | |             {4} | a2  ab  ac  ad  a3   0 0 -a2b 0 |
|                         |                                                   |
|                         |{-2, 4}                                            |
|-------------------------+---------------------------------------------------|
|                         |subquotient ({2} | 0 ab2 abd abd 0 a2c a2c ac2 ab2 |
|                         |             {3} | 0 -ac 0   0   0 -ad -ad 0   -ac |
|                         |             {3} | 0 -a2 ac  ac  0 -ab -ab ad  -a2 |
|                         |             {3} | 0 0   -a2 -a2 0 0   0   -ab 0   |
|                         |                                                   |
|                         |{-2, 3}                                            |
|-------------------------+---------------------------------------------------|
|                         |subquotient (| a2 ab ac ad b2 bc bd c2 cd d2 bc-ad |
|                         |                                                   |
|                         |{-2, 2}                                            |
|                         |                                                   |
|                         |                                                   |
|                         |                                                   |
|-------------------------+---------------------------------------------------|
|                         |0                                                  |
|                         |                                                   |
|                         |{-2, 1}                                            |
|                         |                                                   |
|                         |                                                   |
|                         |                                                   |
|-------------------------+---------------------------------------------------|
|                         |0                                                  |
|                         |                                                   |
|                         |{-2, 0}                                            |
|-------------------------+---------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0 0 0 -acd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -b2d -abd 0 0 0 -bcd 0 0 0 0 0 0|
|0 0 0 ac2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b2c  abc  0 0 0 bc2  0 0 0 0 0 0|
|0 0 0 abc  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b3   ab2  0 0 0 b2c  0 0 0 0 0 0|
|0 0 0 -a2c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -ab2 -a2b 0 0 0 -abc 0 0 0 0 0 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b3  b2d b2d abd abc abc abc bc2 bc2 ac2 b2c b2c bcd bcd bcd 0     bd2 c3  0 b|
|-bc 0   0   0   -bd -bd -bd 0   0   0   -c2 -c2 0   0   0   cd    0   0   0 0|
|-ab bc  bc  ac  -b2 -b2 -b2 bd  bd  ad  -ac -ac c2  c2  c2  bc+ad cd  cd  0 c|
|0   -ab -ab -a2 0   0   0   -b2 -b2 -ab 0   0   -ac -ac -ac -ab   -ad -bc 0 -|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b3-a2c ac2-b2d c3-bd2 a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3 b2c b2d bc2 b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0 0 0 0 0 0 0 0 0 0 0 -c2d -bcd -acd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
| 0 0 0 0 0 0 0 0 0 0 0 c3   bc2  ac2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
| 0 0 0 0 0 0 0 0 0 0 0 bc2  b2c  abc  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
| 0 0 0 0 0 0 0 0 0 0 0 -ac2 -abc -a2c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2 0 acd acd acd c2d c2d 0 0 0        0        0 0 0 0 0 0 0 0 0 0 0 0 0 0   |
|   0 -d2 -d2 -d2 0   0   0 0 -acd     -acd     0 0 0 0 0 0 0 0 0 0 0 0 0 -ac2|
|d  0 -bd -bd -bd d2  d2  0 0 -abc-a2d -abc-a2d 0 0 0 0 0 0 0 0 0 0 0 0 0 b3-a|
|ad 0 0   0   0   -bd -bd 0 0 a2b      a2b      0 0 0 0 0 0 0 0 0 0 0 0 0 0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|cd bd2 c3 c2d cd2 d3 |, | bc-ad b3-a2c ac2-b2d c3-bd2 a3 a2b a2c a2d ab2 abc |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0 0 d  a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0|
| 0 0 -c 0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0|
| 0 0 -b 0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   a|
| 0 0 a  0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|     0 0        0        0 0 0 0 0 0 0       0 0 0 0 0 0 0 0 -b2 -ac -bd -c2 |
|+b2d 0 -bcd     -bcd     0 0 0 0 0 0 -c3+bd2 0 0 0 0 0 0 0 0 c   d   0   0   |
|2c   0 -b2c-abd -b2c-abd 0 0 0 0 0 0 0       0 0 0 0 0 0 0 0 a   b   -c  -d  |
|     0 ab2      ab2      0 0 0 0 0 0 b3-a2c  0 0 0 0 0 0 0 0 0   0   a   b   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|abd ac2 acd ad2 b3 b2c b2d bc2 bcd bd2 c3 c2d cd2 d3 |)                      |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0 |
|   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad|
|b2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0 |
|   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   a|
|0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0|
|0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0|
|0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0  |
|2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd|
|  ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0  |
|  0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0 |
|   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0 |
|   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0 |
|   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0   0   d3 0  0 |
| 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0   0   0  d3 0 |
| bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2 0   0  0  d3|
| 0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0   cd2 0  0  0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0  |
|  0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0  |
|  0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0  |
|2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0  |, {4} | d  a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   a|
| 0  |  {4} | -c 0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0|
| 0  |  {4} | -b 0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0|
| d3 |  {4} | a  0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   a2d 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0   0   d3 0  0  0  |, {|
| 0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0   0   0  d3 0  0  |  {|
| 0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2 0   0  0  d3 0  |  {|
| 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0   cd2 0  0  0  d3 |  {|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|b2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0 |
|   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0 |
|   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0 |
|   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   ac|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2} | -b2 -ac -bd -c2 a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   |
|3} | c   d   0   0   0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   |
|3} | a   b   -c  -d  0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d |
|3} | 0   0   a   b   0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0   0  |
|  0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0   0  |
|  0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc2 0  |
|d 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0   bc2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0|
|0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0|
|0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   a|
|a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0   0   |
| 0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0   0   |
| 0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2 0   |
| 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0   cd2 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0 |
|   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0 |
|cd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc|
|   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d3 0  0  0  |)                                                               |
|0  d3 0  0  |                                                                |
|0  0  d3 0  |                                                                |
|0  0  0  d3 |                                                                |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0  |
|  0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0  |
|2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2|
|  bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-------------------+---------------------------------------------------------|
|                   |subquotient ({5} | 0 0 0 0 0 0 a2 ab ac ad b2 bc bd c2 cd|
|                   |                                                         |
|                   |{-1, 4}                                                  |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|-------------------+---------------------------------------------------------|
| 0   d3 0  0  0  |)|subquotient ({4} | d  ad  0 0 -bd 0 0 0 0 -cd 0 0 0 0 0 0|
| 0   0  d3 0  0  | |             {4} | -c -ac 0 0 bc  0 0 0 0 c2  0 0 0 0 0 0|
| 0   0  0  d3 0  | |             {4} | -b -ab 0 0 b2  0 0 0 0 bc  0 0 0 0 0 0|
| cd2 0  0  0  d3 | |             {4} | a  a2  0 0 -ab 0 0 0 0 -ac 0 0 0 0 0 0|
|                   |                                                         |
|                   |{-1, 3}                                                  |
|-------------------+---------------------------------------------------------|
|                   |subquotient ({2} | 0 0 b2 bd 0 bd 0 ac ac c2 0 0 0      0|
|                   |             {3} | 0 0 -c 0  0 0  0 -d -d 0  0 0 -cd    -|
|                   |             {3} | 0 0 -a c  0 c  0 -b -b d  0 0 -bc-ad -|
|                   |             {3} | 0 0 0  -a 0 -a 0 0  0  -b 0 0 ab     a|
|                   |                                                         |
|                   |{-1, 2}                                                  |
|-------------------+---------------------------------------------------------|
|                   |subquotient (| a b c d bc-ad b3-a2c ac2-b2d c3-bd2 a2 ab |
|                   |                                                         |
|                   |{-1, 1}                                                  |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|-------------------+---------------------------------------------------------|
|                   |0                                                        |
|                   |                                                         |
|                   |{-1, 0}                                                  |
|-------------------+---------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| d2 |, {5} | a2 ab ac ad b2 bc bd c2 cd d2 |)                                |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0 0 0 0 0 0 0 0 0 d  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0|
| 0 0 0 0 0 0 0 0 0 -c 0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0|
| 0 0 0 0 0 0 0 0 0 -b 0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b|
| 0 0 0 0 0 0 0 0 0 a  0  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|      0 0 0 0 0 0 0 0 0 0 0 0 0 -b2 -ac -bd -c2 a2 0  0  0  ab 0  0  0  ac 0 |
|cd    0 0 0 0 0 0 0 0 0 0 0 0 0 c   d   0   0   0  a2 0  0  0  ab 0  0  0  ac|
|bc-ad 0 0 0 0 0 0 0 0 0 0 0 0 0 a   b   -c  -d  0  0  a2 0  0  0  ab 0  0  0 |
|b     0 0 0 0 0 0 0 0 0 0 0 0 0 0   0   a   b   0  0  0  a2 0  0  0  ab 0  0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|ac ad b2 bc bd c2 cd d2 |, | bc-ad b3-a2c ac2-b2d c3-bd2 a2 ab ac ad b2 bc bd|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |, {4} | d  |
|  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |  {4} | -c |
|2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |  {4} | -b |
|  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |  {4} | a  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0|
| 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0|
| ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0|
| 0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  c|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| c2 cd d2 |)                                                                 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0 |
|0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd|
|0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0 |
|0  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  d2 0  0  0  |, {2} | -b2 -ac -bd -c2 a2 0  0  0  ab 0  0  0  ac 0  0  0  ad|
|  0  d2 0  0  |  {3} | c   d   0   0   0  a2 0  0  0  ab 0  0  0  ac 0  0  0 |
|  0  0  d2 0  |  {3} | a   b   -c  -d  0  0  a2 0  0  0  ab 0  0  0  ac 0  0 |
|d 0  0  0  d2 |  {3} | 0   0   a   b   0  0  0  a2 0  0  0  ab 0  0  0  ac 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |)                                |
| 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |                                 |
| bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |                                 |
| 0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |                                 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0|
| ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0|
| 0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d|
| 0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-------+---------------------------------------------------------------------|
|       |0                                                                    |
|       |                                                                     |
|       |{0, 4}                                                               |
|       |                                                                     |
|       |                                                                     |
|       |                                                                     |
|-------+---------------------------------------------------------------------|
|       |subquotient ({5} | a b c d |, {5} | a b c d |)                       |
|       |                                                                     |
|       |{0, 3}                                                               |
|       |                                                                     |
|       |                                                                     |
|       |                                                                     |
|-------+---------------------------------------------------------------------|
|  0  |)|subquotient ({4} | d  d  a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 |, {4} | d  |
|  0  | |             {4} | -c -c 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 |  {4} | -c |
|2 0  | |             {4} | -b -b 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 |  {4} | -b |
|  d2 | |             {4} | a  a  0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d |  {4} | a  |
|       |                                                                     |
|       |{0, 2}                                                               |
|-------+---------------------------------------------------------------------|
|       |subquotient ({2} | ac b2 c2 bd -b2 -ac -bd -c2 a 0 0 0 b 0 0 0 c 0 0 |
|       |             {3} | -d -c 0  0  c   d   0   0   0 a 0 0 0 b 0 0 0 c 0 |
|       |             {3} | -b -a d  c  a   b   -c  -d  0 0 a 0 0 0 b 0 0 0 c |
|       |             {3} | 0  0  -b -a 0   0   a   b   0 0 0 a 0 0 0 b 0 0 0 |
|       |                                                                     |
|       |{0, 1}                                                               |
|-------+---------------------------------------------------------------------|
|       |cokernel | bc-ad b3-a2c ac2-b2d c3-bd2 a b c d |                     |
|       |                                                                     |
|       |{0, 0}                                                               |
|-------+---------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|---------------------------------------------------------------------+       |
|                                                                     |       |
|                                                                     |       |
|                                                                     |       |
|                                                                     |       |
|                                                                     |       |
|                                                                     |       |
|---------------------------------------------------------------------+       |
|                                                                     |       |
|                                                                     |       |
|                                                                     |       |
|                                                                     |       |
|                                                                     |       |
|                                                                     |       |
|---------------------------------------------------------------------+       |
|a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 |)                                   |       |
|0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 |                                    |       |
|0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 |                                    |       |
|0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d |                                    |       |
|                                                                     |       |
|                                                                     |       |
|---------------------------------------------------------------------+       |
|0 d 0 0 0 |, {2} | -b2 -ac -bd -c2 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 |)|       |
|0 0 d 0 0 |  {3} | c   d   0   0   0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 | |       |
|0 0 0 d 0 |  {3} | a   b   -c  -d  0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 | |       |
|c 0 0 0 d |  {3} | 0   0   a   b   0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d | |       |
|                                                                     |       |
|                                                                     |       |
|---------------------------------------------------------------------+       |
|                                                                     |       |
|                                                                     |       |
|                                                                     |       |
|---------------------------------------------------------------------+       |
+-----------------------------------------------------------------------------+

See also
========

  * SpectralSequence ^ ZZ -- the kth page of a
    spectral sequence
  * Examples of filtered complexes and spectral sequences
    -- How to use this package

Ways to use this method:
========================

  * SpectralSequence _ ZZ -- the kth page of a
    spectral sequence
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:3371:0.

spectralSequence(...,Prune=>...)
********************************

Functions with optional argument named Prune:
=============================================

  * page(...,Prune=>...)
  * spectralSequence(...,Prune=>...)
  * spectralSequencePage(...,Prune=>...)
  * spectralSequencePageMap(...,Prune=>...)

Further information
===================

  * Default value: false (Macaulay2Doc),
  * Function: spectralSequence, -- construct a spectral
    sequence
  * Option key: Prune (Macaulay2Doc), -- value of an optional
    argument
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:1075:0.

spectralSequence(FilteredComplex) -- construct a spectral sequence from a filtered complex
******************************************************************************************

  * Function: spectralSequence,
  * Usage:
        E = spectralSequence K
  * Inputs:
      * K, a filtered chain complex, A filtered complex
  * Optional inputs (Macaulay2Doc),:
      * Prune, =>
        ..., default value false,
  * Outputs:
      * E, a spectral sequence,

Description
===========

Returns the spectral sequence associated to the filtered complex.

+---------------------------+
|i1 : A = QQ[x,y];          |
+---------------------------+
|i2 : C = koszul vars A     |
|                           |
|      1      2      1      |
|o2 = A  <-- A  <-- A       |
|                           |
|     0      1      2       |
|                           |
|o2 : ChainComplex          |
+---------------------------+
|i3 : K = filteredComplex C;|
+---------------------------+
|i4 : E = spectralSequence K|
|                           |
|o4 = E                     |
|                           |
|o4 : SpectralSequence      |
+---------------------------+

Ways to use this method:
========================

  * spectralSequence(FilteredComplex)
    -- construct a spectral sequence
    from a filtered complex
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:3189:0.

SpectralSequencePage -- the type of all spectral sequence pages
***************************************************************

Description
===========

A (homological, or lower index) spectral sequence page consists of:

1. A fixed integer $r \geq 0$, the page number;

2. A sequence of modules $\{E^r_{p,q}\}$ for $p,q \in \mathbb{Z}$;

3. A collection of homomorphisms $\{d^r_{p,q}: E^r_{p,q} \rightarrow
E^r_{p-r,q+r-1}\}$ for $p,q \in \mathbb{Z}, r \geq 0$ such that $d^r_{p,q}
d^r_{p+r,q-r+1} = 0$ ;

4. A collection of isomorphisms $E^{r+1}_{p,q}  \rightarrow ker d^r_{p,q} /
image d^r_{p+r,q-r+1}$.

Alternatively a (cohomological, or upper index) spectral sequence page consists
of:

1'.  A fixed integer $r \geq 0$, the page number;

2'. A sequence of modules $\{E_r^{p,q}\}$ for $p,q \in \mathbb{Z}$;

3'. A collection of homomorphisms $\{d_r^{p,q}: E_r^{p,q} \rightarrow
E_r^{p+r,q-r+1}\}$ for $ p,q \in \mathbb{Z}, r \geq 0$ such that $d_r^{p,q}
d_r^{p-r,q+r-1} = 0$ ;

4'. A collection of isomorphisms $E_{r+1}^{p,q}  \rightarrow ker d_r^{p,q} /
image d_r^{p-r,q+r-1}$.

The type SpectralSequencePage is a data type for working with spectral
sequences and spectral sequence pages.

Caveat
======

The isomorphisms $4$ and $4$' are not explicitly part of the data type,
although they can be obtained by using the command homologyIsomorphism.

See also
========

  * SpectralSequence -- the type of all spectral
    sequences
  * SpectralSequencePageMap -- the type of all
    spectral sequence page maps
  * Page -- the type of all pages

Functions and methods returning a spectral sequence page:
=========================================================

  * minimalPresentation(SpectralSequencePage)
    -- a minimal presentation of
    a spectral sequence page
  * "prune(SpectralSequencePage)" -- see
    minimalPresentation(SpectralSequencePage),
    -- a minimal presentation of
    a spectral sequence page
  * spectralSequencePage(FilteredComplex,ZZ)
    -- construct a spectral
    sequence page from a filtered complex

Methods that use a spectral sequence page:
==========================================

  * basis(List,SpectralSequencePage)
    -- generators of a particular
    degree
  * "basis(ZZ,SpectralSequencePage)" -- see
    basis(List,SpectralSequencePage),
    -- generators of a particular degree
  * describe(SpectralSequencePage),
    -- real description
  * hilbertPolynomial(SpectralSequencePage)
    -- the Hilbert polynomial of a
    spectral sequence page
  * net(SpectralSequencePage)
  * page(SpectralSequencePage)
  * pruningMaps(SpectralSequencePage)
    -- compute the pruning maps on a
    spectral sequence page
  * SpectralSequencePage ^ List -- the
    module in the i,j position on the page
  * SpectralSequencePage _ List -- the
    module in the i,j position on the page
  * support(SpectralSequencePage)

For the programmer
==================

The object SpectralSequencePage, is a type (Macaulay2Doc),
with ancestor classes Page, <
MutableHashTable (Macaulay2Doc) < HashTable (Macaulay2Doc)
< Thing (Macaulay2Doc).

-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2239:0.

spectralSequencePage -- construct a spectral sequence page from a filtered complex
**********************************************************************************

  * Usage:
        E = spectralSequencePage(K,r)
  * Inputs:
      * K, a filtered chain complex, A filtered complex
      * r, an integer (Macaulay2Doc),
  * Optional inputs (Macaulay2Doc),:
      * Prune, =>
        ..., default value false,
  * Outputs:
      * E, a spectral sequence page,

Description
===========

This is the primitive spectral sequence page constructor.

+----------------------------------------------------+
|i1 : B = QQ[a..d];                                  |
+----------------------------------------------------+
|i2 : J = ideal vars B;                              |
|                                                    |
|o2 : Ideal of B                                     |
+----------------------------------------------------+
|i3 : C = complete res monomialCurveIdeal(B,{1,3,4});|
+----------------------------------------------------+
|i4 : K = filteredComplex(J,C,4);                    |
+----------------------------------------------------+
|i5 : E = spectralSequence K                         |
|                                                    |
|o5 = E                                              |
|                                                    |
|o5 : SpectralSequence                               |
+----------------------------------------------------+

To view pages and or maps we proceed, for example, as follows

+-----------------------------------------------------------------------------+
|i6 : E^0                                                                     |
|                                                                             |
|     +-----------------------------------------------------------------------|
|o6 = |image | a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab2d abc2|
|     |                                                                       |
|     |{-4, 4}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 3}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 2}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 1}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 0}                                                                |
|     +-----------------------------------------------------------------------|
|                                                                             |
|o6 : SpectralSequencePage                                                    |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 bd3 c4 c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|--------------------------+--------------------------------------------------|
|3d c2d2 cd3 d4 0 0 0 0 0 ||subquotient ({2} | a3 0  0  0  a2b 0   0   0   a2c|
|                          |             {3} | 0  a3 0  0  0   a2b 0   0   0  |
|                          |             {3} | 0  0  a3 0  0   0   a2b 0   0  |
|                          |             {3} | 0  0  0  a3 0   0   0   a2b 0  |
|                          |                                                  |
|                          |{-3, 4}                                           |
|--------------------------+--------------------------------------------------|
|                          |subquotient (| a3 a2b a2c a2d ab2 abc abd ac2 acd |
|                          |                                                  |
|                          |{-3, 3}                                           |
|                          |                                                  |
|                          |                                                  |
|                          |                                                  |
|--------------------------+--------------------------------------------------|
|                          |0                                                 |
|                          |                                                  |
|                          |{-3, 2}                                           |
|                          |                                                  |
|                          |                                                  |
|                          |                                                  |
|--------------------------+--------------------------------------------------|
|                          |0                                                 |
|                          |                                                  |
|                          |{-3, 1}                                           |
|                          |                                                  |
|                          |                                                  |
|                          |                                                  |
|--------------------------+--------------------------------------------------|
|                          |0                                                 |
|                          |                                                  |
|                          |{-3, 0}                                           |
|--------------------------+--------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   |
| a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   |
| 0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   |
| 0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|ad2 b3 b2c b2d bc2 bcd bd2 c3 c2d cd2 d3 a4bc-a5d a4b3-a6c a5c2-a4b2d a4c3-a4|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|ac2 0   0   0   acd 0   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b|
|0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0|
|0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0|
|0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bd2 a3b2c-a4bd a3b4-a5bc a4bc2-a3b3d a3bc3-a3b2d2 a3bc2-a4cd a3b3c-a5c2 a4c3-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2|
|   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0 |
|   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0 |
|   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a3b2cd a3c4-a3bcd2 a3bcd-a4d2 a3b3d-a5cd a4c2d-a3b2d2 a3c3d-a3bd3 a2b3c-a3b2d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d 0   0   0   cd2 0   0   0   d3 0  0  0  -a4b2 -a5c -a4bd -a4c2 -a3b3 -a4bc |
|  c2d 0   0   0   cd2 0   0   0  d3 0  0  a4c   a4d  0     0     a3bc  a3bd  |
|  0   c2d 0   0   0   cd2 0   0  0  d3 0  a5    a4b  -a4c  -a4d  a4b   a3b2  |
|  0   0   c2d 0   0   0   cd2 0  0  0  d3 0     0    a5    a4b   0     0     |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| a2b5-a4b2c a3b2c2-a2b4d a2b2c3-a2b3d2 a2b2c2-a3bcd a2b4c-a4bc2 a3bc3-a2b3cd |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-a3b2d -a3bc2 -a3b2c -a4c2 -a3bcd -a3c3 -a3b2d -a4cd -a3bd2 -a3c2d -a2b4 -a3b|
|0      0      a3c2   a3cd  0      0     a3cd   a3d2  0      0      a2b2c a2b2|
|-a3bc  -a3bd  a4c    a3bc  -a3c2  -a3cd a4d    a3bd  -a3cd  -a3d2  a3b2  a2b3|
|a4b    a3b2   0      0     a4c    a3bc  0      0     a4d    a3bd   0     0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a2bc4-a2b2cd2 a2b2cd-a3bd2 a2b4d-a4bcd a3bc2d-a2b3d2 a2bc3d-a2b2d3 a2bc3-a3c2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2c -a2b3d -a2b2c2 -a2b3c -a3bc2 -a2b2cd -a2bc3 -a2b3d -a3bcd -a2b2d2 -a2bc2d |
|d  0      0       a2bc2  a2bcd  0       0      a2bcd  a2bd2  0       0       |
|   -a2b2c -a2b2d  a3bc   a2b2c  -a2bc2  -a2bcd a3bd   a2b2d  -a2bcd  -a2bd2  |
|   a3b2   a2b3    0      0      a3bc    a2b2c  0      0      a3bd    a2b2d   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d a2b3c2-a4c3 a3c4-a2b2c2d a2c5-a2bc2d2 a2bc2d-a3cd2 a2b3cd-a4c2d a3c3d-a2b2c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-a2b2c2 -a3c3 -a2bc2d -a2c4  -a2b2cd -a3c2d -a2bcd2 -a2c3d -a2b2d2 -a3cd2 -a2|
|a2c3    a2c2d 0       0      a2c2d   a2cd2  0       0      a2cd2   a2d3   0  |
|a3c2    a2bc2 -a2c3   -a2c2d a3cd    a2bcd  -a2c2d  -a2cd2 a3d2    a2bd2  -a2|
|0       0     a3c2    a2bc2  0       0      a3cd    a2bcd  0       0      a3d|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2 a2c4d-a2bcd3 a2bcd2-a3d3 a2b3d2-a4cd2 a3c2d2-a2b2d3 a2c3d2-a2bd4 ab4c-a2b3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|bd3 -a2c2d2 -ab5 -a2b3c -ab4d -ab3c2 -ab4c -a2b2c2 -ab3cd -ab2c3 -ab4d -a2b2c|
|    0       ab3c ab3d   0     0      ab2c2 ab2cd   0      0      ab2cd ab2d2 |
|cd2 -a2d3   a2b3 ab4    -ab3c -ab3d  a2b2c ab3c    -ab2c2 -ab2cd a2b2d ab3d  |
|2   a2bd2   0    0      a2b3  ab4    0     0       a2b2c  ab3c   0     0     |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d ab6-a3b3c a2b3c2-ab5d ab3c3-ab4d2 ab3c2-a2b2cd ab5c-a3b2c2 a2b2c3-ab4cd ab2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d -ab3d2 -ab2c2d -ab3c2 -a2bc3 -ab2c2d -abc4  -ab3cd -a2bc2d -ab2cd2 -abc3d -|
|  0      0       abc3   abc2d  0       0      abc2d  abcd2   0       0      a|
|  -ab2cd -ab2d2  a2bc2  ab2c2  -abc3   -abc2d a2bcd  ab2cd   -abc2d  -abcd2 a|
|  a2b2d  ab3d    0      0      a2bc2   ab2c2  0      0       a2bcd   ab2cd  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c4-ab3cd2 ab3cd-a2b2d2 ab5d-a3b2cd a2b2c2d-ab4d2 ab2c3d-ab3d3 ab2c3-a2bc2d ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|ab3d2 -a2bcd2 -ab2d3 -abc2d2 -ab2c3 -a2c4 -abc3d -ac5  -ab2c2d -a2c3d -abc2d2|
|bcd2  abd3    0      0       ac4    ac3d  0      0     ac3d    ac2d2  0      |
|2bd2  ab2d2   -abcd2 -abd3   a2c3   abc3  -ac4   -ac3d a2c2d   abc2d  -ac3d  |
|      0       a2bd2  ab2d2   0      0     a2c3   abc3  0       0      a2c2d  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|4c2-a3bc3 a2bc4-ab3c2d abc5-ab2c2d2 ab2c2d-a2bcd2 ab4cd-a3bc2d a2bc3d-ab3cd2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| -ac4d  -ab2cd2 -a2c2d2 -abcd3 -ac3d2 -ab2d3 -a2cd3 -abd4 -ac2d3 -b6 -ab4c -b|
| 0      ac2d2   acd3    0      0      acd3   ad4    0     0      b4c b4d   0 |
| -ac2d2 a2cd2   abcd2   -ac2d2 -acd3  a2d3   abd3   -acd3 -ad4   ab4 b5    -b|
| abc2d  0       0       a2cd2  abcd2  0      0      a2d3  abd3   0   0     ab|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|abc4d-ab2cd3 ab2cd2-a2bd3 ab4d2-a3bcd2 a2bc2d2-ab3d3 abc3d2-ab2d4 abc4-a2c3d |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|5d -b4c2 -b5c -ab3c2 -b4cd -b3c3 -b5d -ab3cd -b4d2 -b3c2d -b4c2 -ab2c3 -b3c2d|
|   0     b3c2 b3cd   0     0     b3cd b3d2   0     0      b2c3  b2c2d  0     |
|4c -b4d  ab3c b4c    -b3c2 -b3cd ab3d b4d    -b3cd -b3d2  ab2c2 b3c2   -b2c3 |
|4  b5    0    0      ab3c  b4c   0    0      ab3d  b4d    0     0      ab2c2 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|ab3c3-a3c4 a2c5-ab2c3d ac6-abc3d2 abc3d-a2c2d2 ab3c2d-a3c3d a2c4d-ab2c2d2 ac5|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| -b2c4  -b4cd -ab2c2d -b3cd2 -b2c3d -b4d2 -ab2cd2 -b3d3  -b2c2d2 -b3c3 -abc4 |
| 0      b2c2d b2cd2   0      0      b2cd2 b2d3    0      0       bc4   bc3d  |
| -b2c2d ab2cd b3cd    -b2c2d -b2cd2 ab2d2 b3d2    -b2cd2 -b2d3   abc3  b2c3  |
| b3c2   0     0       ab2cd  b3cd   0     0       ab2d2  b3d2    0     0     |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d-abc2d3 abc2d2-a2cd3 ab3cd2-a3c2d2 a2c3d2-ab2cd3 ac4d2-abcd4 abcd3-a2d4 ab3d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-b2c3d -bc5  -b3c2d -abc3d -b2c2d2 -bc4d  -b3cd2 -abc2d2 -b2cd3 -bc3d2 -b3d3 |
|0      0     bc3d   bc2d2  0       0      bc2d2  bcd3    0      0      bcd3  |
|-bc4   -bc3d abc2d  b2c2d  -bc3d   -bc2d2 abcd2  b2cd2   -bc2d2 -bcd3  abd3  |
|abc3   b2c3  0      0      abc2d   b2c2d  0      0       abcd2  b2cd2  0     |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3-a3cd3 a2c2d3-ab2d4 ac3d3-abd5 b5c-ab4d b7-a2b4c ab4c2-b6d b4c3-b5d2 b4c2-ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-abcd3 -b2d4 -bc2d3 -b2c4 -ac5 -bc4d -c6  -b2c3d -ac4d -bc3d2 -c5d  -b2c2d2 -|
|bd4    0     0      c5    c4d  0     0    c4d    c3d2  0      0     c3d2    c|
|b2d3   -bcd3 -bd4   ac4   bc4  -c5   -c4d ac3d   bc3d  -c4d   -c3d2 ac2d2   b|
|0      abd3  b2d3   0     0    ac4   bc4  0      0     ac3d   bc3d  0       0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3cd b6c-a2b3c2 ab3c3-b5cd b3c4-b4cd2 b4cd-ab3d2 b6d-a2b3cd ab3c2d-b5d2 b3c3d-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|ac3d2 -bc2d3 -c4d2 -b2cd3 -ac2d3 -bcd4 -c3d3 -b2d4 -acd4 -bd5 -c2d4 a4 0  0  |
|2d3   0      0     c2d3   cd4    0     0     cd4   d5    0    0     0  a4 0  |
|c2d2  -c3d2  -c2d3 acd3   bcd3   -c2d3 -cd4  ad4   bd4   -cd4 -d5   0  0  a4 |
|      ac2d2  bc2d2 0      0      acd3  bcd3  0     0     ad4  bd4   0  0  0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b4d3 b3c3-ab2c2d b5c2-a2b2c3 ab2c4-b4c2d b2c5-b3c2d2 b3c2d-ab2cd2 b5cd-a2b2c2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0  a3b 0   0   0   a3c 0   0   0   a3d 0   0   0   a2b2 0    0    0    a2bc 0|
|0  0   a3b 0   0   0   a3c 0   0   0   a3d 0   0   0    a2b2 0    0    0    a|
|0  0   0   a3b 0   0   0   a3c 0   0   0   a3d 0   0    0    a2b2 0    0    0|
|a4 0   0   0   a3b 0   0   0   a3c 0   0   0   a3d 0    0    0    a2b2 0    0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d ab2c3d-b4cd2 b2c4d-b3cd3 b3cd2-ab2d3 b5d2-a2b2cd2 ab2c2d2-b4d3 b2c3d2-b3d4 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d|
|2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0  |
|    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0  |
|    0    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b2c4-abc3d b4c3-a2bc4 abc5-b3c3d bc6-b2c3d2 b2c3d-abc2d2 b4c2d-a2bc3d abc4d-b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2 0    0    0    ab3 0   0   0   ab2c 0    0    0    ab2d 0    0    0    abc2|
|  a2d2 0    0    0   ab3 0   0   0    ab2c 0    0    0    ab2d 0    0    0   |
|  0    a2d2 0    0   0   ab3 0   0    0    ab2c 0    0    0    ab2d 0    0   |
|  0    0    a2d2 0   0   0   ab3 0    0    0    ab2c 0    0    0    ab2d 0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3c2d2 bc5d-b2c2d3 b2c2d2-abcd3 b4cd2-a2bc2d2 abc3d2-b3cd3 bc4d2-b2cd4 b2cd3-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0    0    0    abcd 0    0    0    abd2 0    0    0    ac3 0   0   0   ac2d |
| abc2 0    0    0    abcd 0    0    0    abd2 0    0    0   ac3 0   0   0    |
| 0    abc2 0    0    0    abcd 0    0    0    abd2 0    0   0   ac3 0   0    |
| 0    0    abc2 0    0    0    abcd 0    0    0    abd2 0   0   0   ac3 0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bd4 b4d3-a2bcd3 abc2d3-b3d4 bc3d3-b2d5 bc5-ac4d b3c4-a2c5 ac6-b2c4d c7-bc4d2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0    0    0    acd2 0    0    0    ad3 0   0   0   b4 0  0  0  b3c 0   0   0 |
|ac2d 0    0    0    acd2 0    0    0   ad3 0   0   0  b4 0  0  0   b3c 0   0 |
|0    ac2d 0    0    0    acd2 0    0   0   ad3 0   0  0  b4 0  0   0   b3c 0 |
|0    0    ac2d 0    0    0    acd2 0   0   0   ad3 0  0  0  b4 0   0   0   b3|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bc4d-ac3d2 b3c3d-a2c4d ac5d-b2c3d2 c6d-bc3d3 bc3d2-ac2d3 b3c2d2-a2c3d2 ac4d2-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  b3d 0   0   0   b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0   |
|  0   b3d 0   0   0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0   |
|  0   0   b3d 0   0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0   |
|c 0   0   0   b3d 0    0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b2c2d3 c5d2-bc2d4 bc2d3-acd4 b3cd3-a2c2d3 ac3d3-b2cd4 c4d3-bcd5 bcd4-ad5 b3d4|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| bc3 0   0   0   bc2d 0    0    0    bcd2 0    0    0    bd3 0   0   0   c4 0|
| 0   bc3 0   0   0    bc2d 0    0    0    bcd2 0    0    0   bd3 0   0   0  c|
| 0   0   bc3 0   0    0    bc2d 0    0    0    bcd2 0    0   0   bd3 0   0  0|
| 0   0   0   bc3 0    0    0    bc2d 0    0    0    bcd2 0   0   0   bd3 0  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-a2cd4 ac2d4-b2d5 c3d4-bd6 a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  0  0  c3d 0   0   0   c2d2 0    0    0    cd3 0   0   0   d4 0  0  0  |, {2|
|4 0  0  0   c3d 0   0   0    c2d2 0    0    0   cd3 0   0   0  d4 0  0  |  {3|
|  c4 0  0   0   c3d 0   0    0    c2d2 0    0   0   cd3 0   0  0  d4 0  |  {3|
|  0  c4 0   0   0   c3d 0    0    0    c2d2 0   0   0   cd3 0  0  0  d4 |  {3|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b2c ab2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|} | -a4b2 -a5c -a4bd -a4c2 -a3b3 -a4bc -a3b2d -a3bc2 -a3b2c -a4c2 -a3bcd -a3c|
|} | a4c   a4d  0     0     a3bc  a3bd  0      0      a3c2   a3cd  0      0   |
|} | a5    a4b  -a4c  -a4d  a4b   a3b2  -a3bc  -a3bd  a4c    a3bc  -a3c2  -a3c|
|} | 0     0    a5    a4b   0     0     a4b    a3b2   0      0     a4c    a3bc|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bcd2 bd3 c4 c3d c2d2 cd3 d4 |, | a4bc-a5d a4b3-a6c a5c2-a4b2d a4c3-a4bd2 a3b2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|3 -a3b2d -a4cd -a3bd2 -a3c2d -a2b4 -a3b2c -a2b3d -a2b2c2 -a2b3c -a3bc2 -a2b2c|
|  a3cd   a3d2  0      0      a2b2c a2b2d  0      0       a2bc2  a2bcd  0     |
|d a4d    a3bd  -a3cd  -a3d2  a3b2  a2b3   -a2b2c -a2b2d  a3bc   a2b2c  -a2bc2|
|  0      0     a4d    a3bd   0     0      a3b2   a2b3    0      0      a3bc  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c-a4bd a3b4-a5bc a4bc2-a3b3d a3bc3-a3b2d2 a3bc2-a4cd a3b3c-a5c2 a4c3-a3b2cd a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d -a2bc3 -a2b3d -a3bcd -a2b2d2 -a2bc2d -a2b2c2 -a3c3 -a2bc2d -a2c4  -a2b2cd -|
|  0      a2bcd  a2bd2  0       0       a2c3    a2c2d 0       0      a2c2d   a|
|  -a2bcd a3bd   a2b2d  -a2bcd  -a2bd2  a3c2    a2bc2 -a2c3   -a2c2d a3cd    a|
|  a2b2c  0      0      a3bd    a2b2d   0       0     a3c2    a2bc2  0       0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3c4-a3bcd2 a3bcd-a4d2 a3b3d-a5cd a4c2d-a3b2d2 a3c3d-a3bd3 a2b3c-a3b2d a2b5-a4|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|a3c2d -a2bcd2 -a2c3d -a2b2d2 -a3cd2 -a2bd3 -a2c2d2 -ab5 -a2b3c -ab4d -ab3c2 -|
|2cd2  0       0      a2cd2   a2d3   0      0       ab3c ab3d   0     0      a|
|2bcd  -a2c2d  -a2cd2 a3d2    a2bd2  -a2cd2 -a2d3   a2b3 ab4    -ab3c -ab3d  a|
|      a3cd    a2bcd  0       0      a3d2   a2bd2   0    0      a2b3  ab4    0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b2c a3b2c2-a2b4d a2b2c3-a2b3d2 a2b2c2-a3bcd a2b4c-a4bc2 a3bc3-a2b3cd a2bc4-a2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|ab4c -a2b2c2 -ab3cd -ab2c3 -ab4d -a2b2cd -ab3d2 -ab2c2d -ab3c2 -a2bc3 -ab2c2d|
|b2c2 ab2cd   0      0      ab2cd ab2d2   0      0       abc3   abc2d  0      |
|2b2c ab3c    -ab2c2 -ab2cd a2b2d ab3d    -ab2cd -ab2d2  a2bc2  ab2c2  -abc3  |
|     0       a2b2c  ab3c   0     0       a2b2d  ab3d    0      0      a2bc2  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b2cd2 a2b2cd-a3bd2 a2b4d-a4bcd a3bc2d-a2b3d2 a2bc3d-a2b2d3 a2bc3-a3c2d a2b3c2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| -abc4  -ab3cd -a2bc2d -ab2cd2 -abc3d -ab3d2 -a2bcd2 -ab2d3 -abc2d2 -ab2c3 -a|
| 0      abc2d  abcd2   0       0      abcd2  abd3    0      0       ac4    ac|
| -abc2d a2bcd  ab2cd   -abc2d  -abcd2 a2bd2  ab2d2   -abcd2 -abd3   a2c3   ab|
| ab2c2  0      0       a2bcd   ab2cd  0      0       a2bd2  ab2d2   0      0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-a4c3 a3c4-a2b2c2d a2c5-a2bc2d2 a2bc2d-a3cd2 a2b3cd-a4c2d a3c3d-a2b2cd2 a2c4d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2c4 -abc3d -ac5  -ab2c2d -a2c3d -abc2d2 -ac4d  -ab2cd2 -a2c2d2 -abcd3 -ac3d2 |
|3d  0      0     ac3d    ac2d2  0       0      ac2d2   acd3    0      0      |
|c3  -ac4   -ac3d a2c2d   abc2d  -ac3d   -ac2d2 a2cd2   abcd2   -ac2d2 -acd3  |
|    a2c3   abc3  0       0      a2c2d   abc2d  0       0       a2cd2  abcd2  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-a2bcd3 a2bcd2-a3d3 a2b3d2-a4cd2 a3c2d2-a2b2d3 a2c3d2-a2bd4 ab4c-a2b3d ab6-a3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-ab2d3 -a2cd3 -abd4 -ac2d3 -b6 -ab4c -b5d -b4c2 -b5c -ab3c2 -b4cd -b3c3 -b5d |
|acd3   ad4    0     0      b4c b4d   0    0     b3c2 b3cd   0     0     b3cd |
|a2d3   abd3   -acd3 -ad4   ab4 b5    -b4c -b4d  ab3c b4c    -b3c2 -b3cd ab3d |
|0      0      a2d3  abd3   0   0     ab4  b5    0    0      ab3c  b4c   0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b3c a2b3c2-ab5d ab3c3-ab4d2 ab3c2-a2b2cd ab5c-a3b2c2 a2b2c3-ab4cd ab2c4-ab3cd|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-ab3cd -b4d2 -b3c2d -b4c2 -ab2c3 -b3c2d -b2c4  -b4cd -ab2c2d -b3cd2 -b2c3d -b|
|b3d2   0     0      b2c3  b2c2d  0      0      b2c2d b2cd2   0      0      b2|
|b4d    -b3cd -b3d2  ab2c2 b3c2   -b2c3  -b2c2d ab2cd b3cd    -b2c2d -b2cd2 ab|
|0      ab3d  b4d    0     0      ab2c2  b3c2   0     0       ab2cd  b3cd   0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2 ab3cd-a2b2d2 ab5d-a3b2cd a2b2c2d-ab4d2 ab2c3d-ab3d3 ab2c3-a2bc2d ab4c2-a3bc|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|4d2 -ab2cd2 -b3d3  -b2c2d2 -b3c3 -abc4 -b2c3d -bc5  -b3c2d -abc3d -b2c2d2 -bc|
|cd2 b2d3    0      0       bc4   bc3d  0      0     bc3d   bc2d2  0       0  |
|2d2 b3d2    -b2cd2 -b2d3   abc3  b2c3  -bc4   -bc3d abc2d  b2c2d  -bc3d   -bc|
|    0       ab2d2  b3d2    0     0     abc3   b2c3  0      0      abc2d   b2c|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3 a2bc4-ab3c2d abc5-ab2c2d2 ab2c2d-a2bcd2 ab4cd-a3bc2d a2bc3d-ab3cd2 abc4d-ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|4d  -b3cd2 -abc2d2 -b2cd3 -bc3d2 -b3d3 -abcd3 -b2d4 -bc2d3 -b2c4 -ac5 -bc4d -|
|    bc2d2  bcd3    0      0      bcd3  bd4    0     0      c5    c4d  0     0|
|2d2 abcd2  b2cd2   -bc2d2 -bcd3  abd3  b2d3   -bcd3 -bd4   ac4   bc4  -c5   -|
|2d  0      0       abcd2  b2cd2  0     0      abd3  b2d3   0     0    ac4   b|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2cd3 ab2cd2-a2bd3 ab4d2-a3bcd2 a2bc2d2-ab3d3 abc3d2-ab2d4 abc4-a2c3d ab3c3-a3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c6  -b2c3d -ac4d -bc3d2 -c5d  -b2c2d2 -ac3d2 -bc2d3 -c4d2 -b2cd3 -ac2d3 -bcd4|
|    c4d    c3d2  0      0     c3d2    c2d3   0      0     c2d3   cd4    0    |
|c4d ac3d   bc3d  -c4d   -c3d2 ac2d2   bc2d2  -c3d2  -c2d3 acd3   bcd3   -c2d3|
|c4  0      0     ac3d   bc3d  0       0      ac2d2  bc2d2 0      0      acd3 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c4 a2c5-ab2c3d ac6-abc3d2 abc3d-a2c2d2 ab3c2d-a3c3d a2c4d-ab2c2d2 ac5d-abc2d3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| -c3d3 -b2d4 -acd4 -bd5 -c2d4 a4 0  0  0  a3b 0   0   0   a3c 0   0   0   a3d|
| 0     cd4   d5    0    0     0  a4 0  0  0   a3b 0   0   0   a3c 0   0   0  |
| -cd4  ad4   bd4   -cd4 -d5   0  0  a4 0  0   0   a3b 0   0   0   a3c 0   0  |
| bcd3  0     0     ad4  bd4   0  0  0  a4 0   0   0   a3b 0   0   0   a3c 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| abc2d2-a2cd3 ab3cd2-a3c2d2 a2c3d2-ab2cd3 ac4d2-abcd4 abcd3-a2d4 ab3d3-a3cd3 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   0   0   a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    a2c2|
| a3d 0   0   0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0   |
| 0   a3d 0   0    0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0   |
| 0   0   a3d 0    0    0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a2c2d3-ab2d4 ac3d3-abd5 b5c-ab4d b7-a2b4c ab4c2-b6d b4c3-b5d2 b4c2-ab3cd b6c-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0    0    0    a2cd 0    0    0    a2d2 0    0    0    ab3 0   0   0   ab2c |
| a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0    0   ab3 0   0   0    |
| 0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0   0   ab3 0   0    |
| 0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0   0   0   ab3 0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a2b3c2 ab3c3-b5cd b3c4-b4cd2 b4cd-ab3d2 b6d-a2b3cd ab3c2d-b5d2 b3c3d-b4d3 b3c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0    ab|
|ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0 |
|0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0 |
|0    0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3-ab2c2d b5c2-a2b2c3 ab2c4-b4c2d b2c5-b3c2d2 b3c2d-ab2cd2 b5cd-a2b2c2d ab2c3d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d2 0    0    0    ac3 0   0   0   ac2d 0    0    0    acd2 0    0    0    ad3|
|   abd2 0    0    0   ac3 0   0   0    ac2d 0    0    0    acd2 0    0    0  |
|   0    abd2 0    0   0   ac3 0   0    0    ac2d 0    0    0    acd2 0    0  |
|   0    0    abd2 0   0   0   ac3 0    0    0    ac2d 0    0    0    acd2 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-b4cd2 b2c4d-b3cd3 b3cd2-ab2d3 b5d2-a2b2cd2 ab2c2d2-b4d3 b2c3d2-b3d4 b2c4-abc|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   0   0   b4 0  0  0  b3c 0   0   0   b3d 0   0   0   b2c2 0    0    0    |
| ad3 0   0   0  b4 0  0  0   b3c 0   0   0   b3d 0   0   0    b2c2 0    0    |
| 0   ad3 0   0  0  b4 0  0   0   b3c 0   0   0   b3d 0   0    0    b2c2 0    |
| 0   0   ad3 0  0  0  b4 0   0   0   b3c 0   0   0   b3d 0    0    0    b2c2 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3d b4c3-a2bc4 abc5-b3c3d bc6-b2c3d2 b2c3d-abc2d2 b4c2d-a2bc3d abc4d-b3c2d2 bc|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|b2cd 0    0    0    b2d2 0    0    0    bc3 0   0   0   bc2d 0    0    0    b|
|0    b2cd 0    0    0    b2d2 0    0    0   bc3 0   0   0    bc2d 0    0    0|
|0    0    b2cd 0    0    0    b2d2 0    0   0   bc3 0   0    0    bc2d 0    0|
|0    0    0    b2cd 0    0    0    b2d2 0   0   0   bc3 0    0    0    bc2d 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|5d-b2c2d3 b2c2d2-abcd3 b4cd2-a2bc2d2 abc3d2-b3cd3 bc4d2-b2cd4 b2cd3-abd4 b4d3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|cd2 0    0    0    bd3 0   0   0   c4 0  0  0  c3d 0   0   0   c2d2 0    0   |
|    bcd2 0    0    0   bd3 0   0   0  c4 0  0  0   c3d 0   0   0    c2d2 0   |
|    0    bcd2 0    0   0   bd3 0   0  0  c4 0  0   0   c3d 0   0    0    c2d2|
|    0    0    bcd2 0   0   0   bd3 0  0  0  c4 0   0   0   c3d 0    0    0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-a2bcd3 abc2d3-b3d4 bc3d3-b2d5 bc5-ac4d b3c4-a2c5 ac6-b2c4d c7-bc4d2 bc4d-ac3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0    cd3 0   0   0   d4 0  0  0  |)                                         |
| 0    0   cd3 0   0   0  d4 0  0  |                                          |
| 0    0   0   cd3 0   0  0  d4 0  |                                          |
| c2d2 0   0   0   cd3 0  0  0  d4 |                                          |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2 b3c3d-a2c4d ac5d-b2c3d2 c6d-bc3d3 bc3d2-ac2d3 b3c2d2-a2c3d2 ac4d2-b2c2d3 c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|5d2-bc2d4 bc2d3-acd4 b3cd3-a2c2d3 ac3d3-b2cd4 c4d3-bcd5 bcd4-ad5 b3d4-a2cd4 a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2d4-b2d5 c3d4-bd6 a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab2d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 bd3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|----------------------+------------------------------------------------------|
|                      |subquotient ({4} | a2 0  0  0  ab 0  0  0  ac 0  0  0 |
|                      |             {4} | 0  a2 0  0  0  ab 0  0  0  ac 0  0 |
|                      |             {4} | 0  0  a2 0  0  0  ab 0  0  0  ac 0 |
|                      |             {4} | 0  0  0  a2 0  0  0  ab 0  0  0  ac|
|                      |                                                      |
|                      |{-2, 4}                                               |
|----------------------+------------------------------------------------------|
| c4 c3d c2d2 cd3 d4 |)|subquotient ({2} | a2 0  0  0  ab 0  0  0  ac 0  0  0 |
|                      |             {3} | 0  a2 0  0  0  ab 0  0  0  ac 0  0 |
|                      |             {3} | 0  0  a2 0  0  0  ab 0  0  0  ac 0 |
|                      |             {3} | 0  0  0  a2 0  0  0  ab 0  0  0  ac|
|                      |                                                      |
|                      |{-2, 3}                                               |
|----------------------+------------------------------------------------------|
|                      |subquotient (| a2 ab ac ad b2 bc bd c2 cd d2 a3bc-a4d |
|                      |                                                      |
|                      |{-2, 2}                                               |
|                      |                                                      |
|                      |                                                      |
|                      |                                                      |
|----------------------+------------------------------------------------------|
|                      |0                                                     |
|                      |                                                      |
|                      |{-2, 1}                                               |
|                      |                                                      |
|                      |                                                      |
|                      |                                                      |
|----------------------+------------------------------------------------------|
|                      |0                                                     |
|                      |                                                      |
|                      |{-2, 0}                                               |
|----------------------+------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0|
| 0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d|
| 0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0|
| 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0|
| 0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d|
| 0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0|
| 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a3b3-a5c a4c2-a3b2d a3c3-a3bd2 a2b2c-a3bd a2b4-a4bc a3bc2-a2b3d a2bc3-a2b2d2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  0  0  a3d  a2bd  a2cd  a2d2  ab2d  abcd  abd2  ac2d  acd2  ad3   b3d  b2cd |
|2 0  0  -a3c -a2bc -a2c2 -a2cd -ab2c -abc2 -abcd -ac3  -ac2d -acd2 -b3c -b2c2|
|  d2 0  -a3b -a2b2 -a2bc -a2bd -ab3  -ab2c -ab2d -abc2 -abcd -abd2 -b4  -b3c |
|  0  d2 a4   a3b   a3c   a3d   a2b2  a2bc  a2bd  a2c2  a2cd  a2d2  ab3  ab2c |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  0  0  -a3b2 -a4c -a3bd -a3c2 -a2b3 -a3bc -a2b2d -a2bc2 -a2b2c -a3c2 -a2bcd |
|2 0  0  a3c   a3d  0     0     a2bc  a2bd  0      0      a2c2   a2cd  0      |
|  d2 0  a4    a3b  -a3c  -a3d  a3b   a2b2  -a2bc  -a2bd  a3c    a2bc  -a2c2  |
|  0  d2 0     0    a4    a3b   0     0     a3b    a2b2   0      0     a3c    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a2bc2-a3cd a2b3c-a4c2 a3c3-a2b2cd a2c4-a2bcd2 a2bcd-a3d2 a2b3d-a4cd a3c2d-a2b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| b2d2  bc2d  bcd2  bd3   c3d  c2d2  cd3   d4   a3 0  0  0  a2b 0   0   0   a2|
| -b2cd -bc3  -bc2d -bcd2 -c4  -c3d  -c2d2 -cd3 0  a3 0  0  0   a2b 0   0   0 |
| -b3d  -b2c2 -b2cd -b2d2 -bc3 -bc2d -bcd2 -bd3 0  0  a3 0  0   0   a2b 0   0 |
| ab2d  abc2  abcd  abd2  ac3  ac2d  acd2  ad3  0  0  0  a3 0   0   0   a2b 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-a2c3 -a2b2d -a3cd -a2bd2 -a2c2d -ab4 -a2b2c -ab3d -ab2c2 -ab3c -a2bc2 -ab2cd|
|0     a2cd   a2d2  0      0      ab2c ab2d   0     0      abc2  abcd   0     |
|-a2cd a3d    a2bd  -a2cd  -a2d2  a2b2 ab3    -ab2c -ab2d  a2bc  ab2c   -abc2 |
|a2bc  0      0     a3d    a2bd   0    0      a2b2  ab3    0     0      a2bc  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2d2 a2c3d-a2bd3 ab3c-a2b2d ab5-a3b2c a2b2c2-ab4d ab2c3-ab3d2 ab2c2-a2bcd ab4c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0  |
|  a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0  |
|  0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0  |
|  0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| -abc3 -ab3d -a2bcd -ab2d2 -abc2d -ab2c2 -a2c3 -abc2d -ac4  -ab2cd -a2c2d -ab|
| 0     abcd  abd2   0      0      ac3    ac2d  0      0     ac2d   acd2   0  |
| -abcd a2bd  ab2d   -abcd  -abd2  a2c2   abc2  -ac3   -ac2d a2cd   abcd   -ac|
| ab2c  0     0      a2bd   ab2d   0      0     a2c2   abc2  0      0      a2c|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-a3bc2 a2bc3-ab3cd abc4-ab2cd2 ab2cd-a2bd2 ab4d-a3bcd a2bc2d-ab3d2 abc3d-ab2d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| ac2 0   0   0   acd 0   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   |
| 0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   |
| 0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   |
| 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|cd2 -ac3d -ab2d2 -a2cd2 -abd3 -ac2d2 -b5 -ab3c -b4d -b3c2 -b4c -ab2c2 -b3cd -|
|    0     acd2   ad3    0     0      b3c b3d   0    0     b2c2 b2cd   0     0|
|2d  -acd2 a2d2   abd2   -acd2 -ad3   ab3 b4    -b3c -b3d  ab2c b3c    -b2c2 -|
|d   abcd  0      0      a2d2  abd2   0   0     ab3  b4    0    0      ab2c  b|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3 abc3-a2c2d ab3c2-a3c3 a2c4-ab2c2d ac5-abc2d2 abc2d-a2cd2 ab3cd-a3c2d a2c3d-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c|
|0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0|
|0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0|
|0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b2c3 -b4d -ab2cd -b3d2 -b2c2d -b3c2 -abc3 -b2c2d -bc4  -b3cd -abc2d -b2cd2 -b|
|     b2cd b2d2   0     0      bc3   bc2d  0      0     bc2d  bcd2   0      0 |
|b2cd ab2d b3d    -b2cd -b2d2  abc2  b2c2  -bc3   -bc2d abcd  b2cd   -bc2d  -b|
|3c   0    0      ab2d  b3d    0     0     abc2   b2c2  0     0      abcd   b2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|ab2cd2 ac4d-abcd3 abcd2-a2d3 ab3d2-a3cd2 a2c2d2-ab2d3 ac3d2-abd4 b4c-ab3d b6-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2d 0   0   0   cd2 0   0   0   d3 0  0  0  |, {4} | a3d  a2bd  a2cd  a2d2  ab|
|   c2d 0   0   0   cd2 0   0   0  d3 0  0  |  {4} | -a3c -a2bc -a2c2 -a2cd -a|
|   0   c2d 0   0   0   cd2 0   0  0  d3 0  |  {4} | -a3b -a2b2 -a2bc -a2bd -a|
|   0   0   c2d 0   0   0   cd2 0  0  0  d3 |  {4} | a4   a3b   a3c   a3d   a2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c3d -b3d2 -abcd2 -b2d3 -bc2d2 -b2c3 -ac4 -bc3d -c5  -b2c2d -ac3d -bc2d2 -c4d |
|    bcd2  bd3    0     0      c4    c3d  0     0    c3d    c2d2  0      0    |
|cd2 abd2  b2d2   -bcd2 -bd3   ac3   bc3  -c4   -c3d ac2d   bc2d  -c3d   -c2d2|
|cd  0     0      abd2  b2d2   0     0    ac3   bc3  0      0     ac2d   bc2d |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a2b3c ab3c2-b5d b3c3-b4d2 b3c2-ab2cd b5c-a2b2c2 ab2c3-b4cd b2c4-b3cd2 b3cd-ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2d  abcd  abd2  ac2d  acd2  ad3   b3d  b2cd  b2d2  bc2d  bcd2  bd3   c3d  c2d|
|b2c -abc2 -abcd -ac3  -ac2d -acd2 -b3c -b2c2 -b2cd -bc3  -bc2d -bcd2 -c4  -c3|
|b3  -ab2c -ab2d -abc2 -abcd -abd2 -b4  -b3c  -b3d  -b2c2 -b2cd -b2d2 -bc3 -bc|
|b2  a2bc  a2bd  a2c2  a2cd  a2d2  ab3  ab2c  ab2d  abc2  abcd  abd2  ac3  ac2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| -b2cd2 -ac2d2 -bcd3 -c3d2 -b2d3 -acd3 -bd4 -c2d3 a3 0  0  0  a2b 0   0   0  |
| c2d2   cd3    0     0     cd3   d4    0    0     0  a3 0  0  0   a2b 0   0  |
| acd2   bcd2   -c2d2 -cd3  ad3   bd3   -cd3 -d4   0  0  a3 0  0   0   a2b 0  |
| 0      0      acd2  bcd2  0     0     ad3  bd3   0  0  0  a3 0   0   0   a2b|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2d2 b5d-a2b2cd ab2c2d-b4d2 b2c3d-b3d3 b2c3-abc2d b4c2-a2bc3 abc4-b3c2d bc5-b2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2  cd3   d4   a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2|
|d  -c2d2 -cd3 0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0  |
|2d -bcd2 -bd3 0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0  |
|d  acd2  ad3  0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   a2d 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   |
| 0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   |
| 0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd |
| 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2d2 b2c2d-abcd2 b4cd-a2bc2d abc3d-b3cd2 bc4d-b2cd3 b2cd2-abd3 b4d2-a2bcd2 ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   |
| ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   |
| 0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   |
| 0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0|
|0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0|
|0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0|
|abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2d2-b3d3 bc3d2-b2d4 bc4-ac3d b3c3-a2c4 ac5-b2c3d c6-bc3d2 bc3d-ac2d2 b3c2d-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   b|
|0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0|
|0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0|
|0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0   bc2 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0|
|   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0|
|   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0|
|2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2c3d ac4d-b2c2d2 c5d-bc2d3 bc2d2-acd3 b3cd2-a2c2d2 ac3d2-b2cd3 c4d2-bcd4 bcd3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|cd 0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0   0   d3|
|   bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0   0   0 |
|   0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2 0   0 |
|   0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0   cd2 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  c2d 0   0   0   cd2 0   0   0   d3 0  0  0  |, {2} | -a3b2 -a4c -a3bd -a3c2|
|  0   c2d 0   0   0   cd2 0   0   0  d3 0  0  |  {3} | a3c   a3d  0     0    |
|  0   0   c2d 0   0   0   cd2 0   0  0  d3 0  |  {3} | a4    a3b  -a3c  -a3d |
|3 0   0   0   c2d 0   0   0   cd2 0  0  0  d3 |  {3} | 0     0    a4    a3b  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-ad4 b3d3-a2cd3 ac2d3-b2d4 c3d3-bd5 a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0  0  0  |)                                                                 |
| d3 0  0  |                                                                  |
| 0  d3 0  |                                                                  |
| 0  0  d3 |                                                                  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| -a2b3 -a3bc -a2b2d -a2bc2 -a2b2c -a3c2 -a2bcd -a2c3 -a2b2d -a3cd -a2bd2 -a2c|
| a2bc  a2bd  0      0      a2c2   a2cd  0      0     a2cd   a2d2  0      0   |
| a3b   a2b2  -a2bc  -a2bd  a3c    a2bc  -a2c2  -a2cd a3d    a2bd  -a2cd  -a2d|
| 0     0     a3b    a2b2   0      0     a3c    a2bc  0      0     a3d    a2bd|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| b2c b2d bc2 bcd bd2 c3 c2d cd2 d3 |, | a3bc-a4d a3b3-a5c a4c2-a3b2d a3c3-a3b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2d -ab4 -a2b2c -ab3d -ab2c2 -ab3c -a2bc2 -ab2cd -abc3 -ab3d -a2bcd -ab2d2 -ab|
|   ab2c ab2d   0     0      abc2  abcd   0      0     abcd  abd2   0      0  |
|2  a2b2 ab3    -ab2c -ab2d  a2bc  ab2c   -abc2  -abcd a2bd  ab2d   -abcd  -ab|
|   0    0      a2b2  ab3    0     0      a2bc   ab2c  0     0      a2bd   ab2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2 a2b2c-a3bd a2b4-a4bc a3bc2-a2b3d a2bc3-a2b2d2 a2bc2-a3cd a2b3c-a4c2 a3c3-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2d -ab2c2 -a2c3 -abc2d -ac4  -ab2cd -a2c2d -abcd2 -ac3d -ab2d2 -a2cd2 -abd3 |
|    ac3    ac2d  0      0     ac2d   acd2   0      0     acd2   ad3    0     |
|d2  a2c2   abc2  -ac3   -ac2d a2cd   abcd   -ac2d  -acd2 a2d2   abd2   -acd2 |
|d   0      0     a2c2   abc2  0      0      a2cd   abcd  0      0      a2d2  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2b2cd a2c4-a2bcd2 a2bcd-a3d2 a2b3d-a4cd a3c2d-a2b2d2 a2c3d-a2bd3 ab3c-a2b2d a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-ac2d2 -b5 -ab3c -b4d -b3c2 -b4c -ab2c2 -b3cd -b2c3 -b4d -ab2cd -b3d2 -b2c2d |
|0      b3c b3d   0    0     b2c2 b2cd   0     0     b2cd b2d2   0     0      |
|-ad3   ab3 b4    -b3c -b3d  ab2c b3c    -b2c2 -b2cd ab2d b3d    -b2cd -b2d2  |
|abd2   0   0     ab3  b4    0    0      ab2c  b3c   0    0      ab2d  b3d    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b5-a3b2c a2b2c2-ab4d ab2c3-ab3d2 ab2c2-a2bcd ab4c-a3bc2 a2bc3-ab3cd abc4-ab2c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-b3c2 -abc3 -b2c2d -bc4  -b3cd -abc2d -b2cd2 -bc3d -b3d2 -abcd2 -b2d3 -bc2d2 |
|bc3   bc2d  0      0     bc2d  bcd2   0      0     bcd2  bd3    0     0      |
|abc2  b2c2  -bc3   -bc2d abcd  b2cd   -bc2d  -bcd2 abd2  b2d2   -bcd2 -bd3   |
|0     0     abc2   b2c2  0     0      abcd   b2cd  0     0      abd2  b2d2   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2 ab2cd-a2bd2 ab4d-a3bcd a2bc2d-ab3d2 abc3d-ab2d3 abc3-a2c2d ab3c2-a3c3 a2c4|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-b2c3 -ac4 -bc3d -c5  -b2c2d -ac3d -bc2d2 -c4d  -b2cd2 -ac2d2 -bcd3 -c3d2 -b2|
|c4    c3d  0     0    c3d    c2d2  0      0     c2d2   cd3    0     0     cd3|
|ac3   bc3  -c4   -c3d ac2d   bc2d  -c3d   -c2d2 acd2   bcd2   -c2d2 -cd3  ad3|
|0     0    ac3   bc3  0      0     ac2d   bc2d  0      0      acd2  bcd2  0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-ab2c2d ac5-abc2d2 abc2d-a2cd2 ab3cd-a3c2d a2c3d-ab2cd2 ac4d-abcd3 abcd2-a2d3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d3 -acd3 -bd4 -c2d3 a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   0|
|   d4    0    0     0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   0|
|   bd3   -cd3 -d4   0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d 0|
|   0     ad3  bd3   0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   a|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| ab3d2-a3cd2 a2c2d2-ab2d3 ac3d2-abd4 b4c-ab3d b6-a2b3c ab3c2-b5d b3c3-b4d2 b3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0 |
|   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0 |
|   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   ac|
|2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2-ab2cd b5c-a2b2c2 ab2c3-b4cd b2c4-b3cd2 b3cd-ab2d2 b5d-a2b2cd ab2c2d-b4d2 b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0  |
|  0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0  |
|d 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc2|
|  acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2c3d-b3d3 b2c3-abc2d b4c2-a2bc3 abc4-b3c2d bc5-b2c2d2 b2c2d-abcd2 b4cd-a2bc2d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0   |
| 0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0   |
| 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2 |
| bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| abc3d-b3cd2 bc4d-b2cd3 b2cd2-abd3 b4d2-a2bcd2 abc2d2-b3d3 bc3d2-b2d4 bc4-ac3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|0   d3 0  0  0  |)                                                           |
|0   0  d3 0  0  |                                                            |
|0   0  0  d3 0  |                                                            |
|cd2 0  0  0  d3 |                                                            |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d b3c3-a2c4 ac5-b2c3d c6-bc3d2 bc3d-ac2d2 b3c2d-a2c3d ac4d-b2c2d2 c5d-bc2d3 b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2d2-acd3 b3cd2-a2c2d2 ac3d2-b2cd3 c4d2-bcd4 bcd3-ad4 b3d3-a2cd3 ac2d3-b2d4 c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3d3-bd5 a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3 b2c b2d bc2 bcd bd2 c3 c2d |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|---------+-------------------------------------------------------------------|
|         |subquotient ({5} | a b c d a2 ab ac ad b2 bc bd c2 cd d2 |, {5} | a|
|         |                                                                   |
|         |{-1, 4}                                                            |
|         |                                                                   |
|         |                                                                   |
|         |                                                                   |
|---------+-------------------------------------------------------------------|
|         |subquotient ({4} | a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 a2d  abd  acd  a|
|         |             {4} | 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 -a2c -abc -ac2 -|
|         |             {4} | 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 -a2b -ab2 -abc -|
|         |             {4} | 0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d a3   a2b  a2c  a|
|         |                                                                   |
|         |{-1, 3}                                                            |
|---------+-------------------------------------------------------------------|
|cd2 d3 |)|subquotient ({2} | a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 -a2b2 -a3c -a2bd|
|         |             {3} | 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 a2c   a2d  0    |
|         |             {3} | 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 a3    a2b  -a2c |
|         |             {3} | 0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0     0    a3   |
|         |                                                                   |
|         |{-1, 2}                                                            |
|---------+-------------------------------------------------------------------|
|         |subquotient (| a b c d a2bc-a3d a2b3-a4c a3c2-a2b2d a2c3-a2bd2 ab2c|
|         |                                                                   |
|         |{-1, 1}                                                            |
|         |                                                                   |
|         |                                                                   |
|         |                                                                   |
|---------+-------------------------------------------------------------------|
|         |0                                                                  |
|         |                                                                   |
|         |{-1, 0}                                                            |
|---------+-------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2 ab ac ad b2 bc bd c2 cd d2 |)                                              |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2  b2d  bcd  bd2  c2d  cd2  d3   a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0|
|acd -b2c -bc2 -bcd -c3  -c2d -cd2 0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0|
|abd -b3  -b2c -b2d -bc2 -bcd -bd2 0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  a|
|2d  ab2  abc  abd  ac2  acd  ad2  0  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| -a2c2 -ab3 -a2bc -ab2d -abc2 -ab2c -a2c2 -abcd -ac3 -ab2d -a2cd -abd2 -ac2d |
| 0     abc  abd   0     0     ac2   acd   0     0    acd   ad2   0     0     |
| -a2d  a2b  ab2   -abc  -abd  a2c   abc   -ac2  -acd a2d   abd   -acd  -ad2  |
| a2b   0    0     a2b   ab2   0     0     a2c   abc  0     0     a2d   abd   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-a2bd ab4-a3bc a2bc2-ab3d abc3-ab2d2 abc2-a2cd ab3c-a3c2 a2c3-ab2cd ac4-abcd2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |
|  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |
|d 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |
|  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-b4 -ab2c -b3d -b2c2 -b3c -abc2 -b2cd -bc3 -b3d -abcd -b2d2 -bc2d -b2c2 -ac3 |
|b2c b2d   0    0     bc2  bcd   0     0    bcd  bd2   0     0     c3    c2d  |
|ab2 b3    -b2c -b2d  abc  b2c   -bc2  -bcd abd  b2d   -bcd  -bd2  ac2   bc2  |
|0   0     ab2  b3    0    0     abc   b2c  0    0     abd   b2d   0     0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| abcd-a2d2 ab3d-a3cd a2c2d-ab2d2 ac3d-abd3 b3c-ab2d b5-a2b2c ab2c2-b4d b2c3-b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
||, {4} | a2d  abd  acd  ad2  b2d  bcd  bd2  c2d  cd2  d3   a2 0  0  0  ab 0  |
||  {4} | -a2c -abc -ac2 -acd -b2c -bc2 -bcd -c3  -c2d -cd2 0  a2 0  0  0  ab |
||  {4} | -a2b -ab2 -abc -abd -b3  -b2c -b2d -bc2 -bcd -bd2 0  0  a2 0  0  0  |
||  {4} | a3   a2b  a2c  a2d  ab2  abc  abd  ac2  acd  ad2  0  0  0  a2 0  0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-bc2d -c4  -b2cd -ac2d -bcd2 -c3d -b2d2 -acd2 -bd3 -c2d2 a2 0  0  0  ab 0  0 |
|0     0    c2d   cd2   0     0    cd2   d3    0    0     0  a2 0  0  0  ab 0 |
|-c3   -c2d acd   bcd   -c2d  -cd2 ad2   bd2   -cd2 -d3   0  0  a2 0  0  0  ab|
|ac2   bc2  0     0     acd   bcd  0     0     ad2  bd2   0  0  0  a2 0  0  0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3d2 b2c2-abcd b4c-a2bc2 abc3-b3cd bc4-b2cd2 b2cd-abd2 b4d-a2bcd abc2d-b3d2 bc|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0 |
|0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0 |
|ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0 |
|0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  c|
| 0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0|
| 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0|
| ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3d-b2d3 bc3-ac2d b3c2-a2c3 ac4-b2c2d c5-bc2d2 bc2d-acd2 b3cd-a2c2d ac3d-b2cd2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| cd 0  0  0  d2 0  0  0  |)                                                  |
| 0  cd 0  0  0  d2 0  0  |                                                   |
| 0  0  cd 0  0  0  d2 0  |                                                   |
| 0  0  0  cd 0  0  0  d2 |                                                   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d 0  0  0  d2 0  0  0  |, {2} | -a2b2 -a3c -a2bd -a2c2 -ab3 -a2bc -ab2d -abc2|
|  cd 0  0  0  d2 0  0  |  {3} | a2c   a2d  0     0     abc  abd   0     0    |
|  0  cd 0  0  0  d2 0  |  {3} | a3    a2b  -a2c  -a2d  a2b  ab2   -abc  -abd |
|  0  0  cd 0  0  0  d2 |  {3} | 0     0    a3    a2b   0    0     a2b   ab2  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| c4d-bcd3 bcd2-ad3 b3d2-a2cd2 ac2d2-b2d3 c3d2-bd4 a2 ab ac ad b2 bc bd c2 cd |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| -ab2c -a2c2 -abcd -ac3 -ab2d -a2cd -abd2 -ac2d -b4 -ab2c -b3d -b2c2 -b3c -ab|
| ac2   acd   0     0    acd   ad2   0     0     b2c b2d   0    0     bc2  bcd|
| a2c   abc   -ac2  -acd a2d   abd   -acd  -ad2  ab2 b3    -b2c -b2d  abc  b2c|
| 0     0     a2c   abc  0     0     a2d   abd   0   0     ab2  b3    0    0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2 |, | a2bc-a3d a2b3-a4c a3c2-a2b2d a2c3-a2bd2 ab2c-a2bd ab4-a3bc a2bc2-ab3d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2 -b2cd -bc3 -b3d -abcd -b2d2 -bc2d -b2c2 -ac3 -bc2d -c4  -b2cd -ac2d -bcd2 |
|   0     0    bcd  bd2   0     0     c3    c2d  0     0    c2d   cd2   0     |
|   -bc2  -bcd abd  b2d   -bcd  -bd2  ac2   bc2  -c3   -c2d acd   bcd   -c2d  |
|   abc   b2c  0    0     abd   b2d   0     0    ac2   bc2  0     0     acd   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| abc3-ab2d2 abc2-a2cd ab3c-a3c2 a2c3-ab2cd ac4-abcd2 abcd-a2d2 ab3d-a3cd a2c2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-c3d -b2d2 -acd2 -bd3 -c2d2 a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b|
|0    cd2   d3    0    0     0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0|
|-cd2 ad2   bd2   -cd2 -d3   0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0|
|bcd  0     0     ad2  bd2   0  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d-ab2d2 ac3d-abd3 b3c-ab2d b5-a2b2c ab2c2-b4d b2c3-b3d2 b2c2-abcd b4c-a2bc2 a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |)    |
|  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |     |
|  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |     |
|  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |     |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bc3-b3cd bc4-b2cd2 b2cd-abd2 b4d-a2bcd abc2d-b3d2 bc3d-b2d3 bc3-ac2d b3c2-a2c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3 ac4-b2c2d c5-bc2d2 bc2d-acd2 b3cd-a2c2d ac3d-b2cd2 c4d-bcd3 bcd2-ad3 b3d2-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|---------------------------------------------------------+-------------------|
|                                                         |0                  |
|                                                         |                   |
|                                                         |{0, 4}             |
|                                                         |                   |
|                                                         |                   |
|                                                         |                   |
|---------------------------------------------------------+-------------------|
|                                                         |cokernel {5} | a b |
|                                                         |                   |
|                                                         |{0, 3}             |
|                                                         |                   |
|                                                         |                   |
|                                                         |                   |
|---------------------------------------------------------+-------------------|
|                                                         |cokernel {4} | ad  |
|                                                         |         {4} | -ac |
|                                                         |         {4} | -ab |
|                                                         |         {4} | a2  |
|                                                         |                   |
|                                                         |{0, 2}             |
|---------------------------------------------------------+-------------------|
|2cd2 ac2d2-b2d3 c3d2-bd4 a2 ab ac ad b2 bc bd c2 cd d2 |)|cokernel {2} | -ab2|
|                                                         |         {3} | ac  |
|                                                         |         {3} | a2  |
|                                                         |         {3} | 0   |
|                                                         |                   |
|                                                         |{0, 1}             |
|---------------------------------------------------------+-------------------|
|                                                         |cokernel | abc-a2d |
|                                                         |                   |
|                                                         |{0, 0}             |
|---------------------------------------------------------+-------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c d |                                                                        |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bd  cd  d2  a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 |                                |
|-bc -c2 -cd 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 |                                |
|-b2 -bc -bd 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 |                                |
|ab  ac  ad  0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d |                                |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| -a2c -abd -ac2 -b3 -abc -b2d -bc2 -b2c -ac2 -bcd -c3 -b2d -acd -bd2 -c2d a 0|
| ad   0    0    bc  bd   0    0    c2   cd   0    0   cd   d2   0    0    0 a|
| ab   -ac  -ad  ab  b2   -bc  -bd  ac   bc   -c2  -cd ad   bd   -cd  -d2  0 0|
| 0    a2   ab   0   0    ab   b2   0    0    ac   bc  0    0    ad   bd   0 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|ab3-a3c a2c2-ab2d ac3-abd2 b2c-abd b4-a2bc abc2-b3d bc3-b2d2 bc2-acd b3c-a2c2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|--------------------------------------------------------------+              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|--------------------------------------------------------------+              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|--------------------------------------------------------------+              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|--------------------------------------------------------------+              |
| 0 0 b 0 0 0 c 0 0 0 d 0 0 0 |                                |              |
| 0 0 0 b 0 0 0 c 0 0 0 d 0 0 |                                |              |
| a 0 0 0 b 0 0 0 c 0 0 0 d 0 |                                |              |
| 0 a 0 0 0 b 0 0 0 c 0 0 0 d |                                |              |
|                                                              |              |
|                                                              |              |
|--------------------------------------------------------------+              |
| ac3-b2cd c4-bcd2 bcd-ad2 b3d-a2cd ac2d-b2d2 c3d-bd3 a b c d ||              |
|                                                              |              |
|                                                              |              |
|--------------------------------------------------------------+              |
+-----------------------------------------------------------------------------+

See also
========

  * spectralSequence -- construct a spectral sequence
  * spectralSequence(FilteredComplex)
    -- construct a spectral sequence
    from a filtered complex
  * SpectralSequencePageMap -- the type of all
    spectral sequence page maps
  * Examples of filtered complexes and spectral sequences
    -- How to use this package

Ways to use spectralSequencePage:
=================================

  * spectralSequencePage(FilteredComplex,ZZ)
    -- construct a spectral
    sequence page from a filtered complex

For the programmer
==================

The object spectralSequencePage, is a method function with options (Macaulay2Doc).

-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2748:0.

SpectralSequencePage ^ List -- the module in the i,j position on the page
*************************************************************************

  * Operator: ^ (Macaulay2Doc),
  * Usage:
        M = P^L
  * Inputs:
      * P, a spectral sequence page,
      * L, a list (Macaulay2Doc), A list L = \{i,j\} of integers
  * Outputs:
      * M, a module (Macaulay2Doc),

Description
===========

Returns the module in the \{i,j\}  \ position in the spectral sequence page.
(Using cohomological or upper indexing conventions.)  The relationship
$E^{-i,-j} = E_{i,j}$ holds.

+-------------------------------------------------------+
|i1 : A = QQ[x,y]                                       |
|                                                       |
|o1 = A                                                 |
|                                                       |
|o1 : PolynomialRing                                    |
+-------------------------------------------------------+
|i2 : C = koszul vars A;                                |
+-------------------------------------------------------+
|i3 : K = filteredComplex C;                            |
+-------------------------------------------------------+
|i4 : E = spectralSequence K                            |
|                                                       |
|o4 = E                                                 |
|                                                       |
|o4 : SpectralSequence                                  |
+-------------------------------------------------------+
|i5 : E_0                                               |
|                                                       |
|     +-----------------+-----------------------+------+|
|     |                 |                       | 1    ||
|o5 = |image | 1 0 0 0 ||image {1} | 1 0 0 0 0 ||A     ||
|     |                 |      {1} | 0 1 0 0 0 ||      ||
|     |{0, 0}           |                       |{2, 0}||
|     |                 |{1, 0}                 |      ||
|     +-----------------+-----------------------+------+|
|                                                       |
|o5 : SpectralSequencePage                              |
+-------------------------------------------------------+
|i6 : E_0 ^{-1,0}                                       |
|                                                       |
|o6 = image {1} | 1 0 0 0 0 |                           |
|           {1} | 0 1 0 0 0 |                           |
|                                                       |
|                             2                         |
|o6 : A-module, submodule of A                          |
+-------------------------------------------------------+
|i7 : E^0 _{1,0}                                        |
|                                                       |
|o7 = image {1} | 1 0 0 0 0 |                           |
|           {1} | 0 1 0 0 0 |                           |
|                                                       |
|                             2                         |
|o7 : A-module, submodule of A                          |
+-------------------------------------------------------+

See also
========

  * Examples of filtered complexes and spectral sequences
    -- How to use this package

Ways to use this method:
========================

  * SpectralSequencePage ^ List -- the
    module in the i,j position on the page
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:3527:0.

SpectralSequencePage _ List -- the module in the i,j position on the page
*************************************************************************

  * Operator: _ (Macaulay2Doc),
  * Usage:
        M = P_L
  * Inputs:
      * P, a spectral sequence page,
      * L, a list (Macaulay2Doc), A list L = \{i,j\} \ of integers
  * Outputs:
      * M, a module (Macaulay2Doc),

Description
===========

Returns the module in the \{i,j\} \ position in the spectral sequence page.
(Using homological or lower indexing conventions.)  The relationship $E_{i,j} =
E^{-i,-j}$ holds.

+-------------------------------------------------------+
|i1 : A = QQ[x,y]                                       |
|                                                       |
|o1 = A                                                 |
|                                                       |
|o1 : PolynomialRing                                    |
+-------------------------------------------------------+
|i2 : C = koszul vars A;                                |
+-------------------------------------------------------+
|i3 : K = filteredComplex C;                            |
+-------------------------------------------------------+
|i4 : E = spectralSequence K                            |
|                                                       |
|o4 = E                                                 |
|                                                       |
|o4 : SpectralSequence                                  |
+-------------------------------------------------------+
|i5 : E^0                                               |
|                                                       |
|     +-----------------+-----------------------+------+|
|     |                 |                       | 1    ||
|o5 = |image | 1 0 0 0 ||image {1} | 1 0 0 0 0 ||A     ||
|     |                 |      {1} | 0 1 0 0 0 ||      ||
|     |{0, 0}           |                       |{2, 0}||
|     |                 |{1, 0}                 |      ||
|     +-----------------+-----------------------+------+|
|                                                       |
|o5 : SpectralSequencePage                              |
+-------------------------------------------------------+
|i6 : E^0 _{1,0}                                        |
|                                                       |
|o6 = image {1} | 1 0 0 0 0 |                           |
|           {1} | 0 1 0 0 0 |                           |
|                                                       |
|                             2                         |
|o6 : A-module, submodule of A                          |
+-------------------------------------------------------+
|i7 : E_0 ^{-1,0}                                       |
|                                                       |
|o7 = image {1} | 1 0 0 0 0 |                           |
|           {1} | 0 1 0 0 0 |                           |
|                                                       |
|                             2                         |
|o7 : A-module, submodule of A                          |
+-------------------------------------------------------+

See also
========

  * Examples of filtered complexes and spectral sequences
    -- How to use this package

Ways to use this method:
========================

  * SpectralSequencePage _ List -- the
    module in the i,j position on the page
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:3557:0.

spectralSequencePage(...,Prune=>...)
************************************

Functions with optional argument named Prune:
=============================================

  * page(...,Prune=>...)
  * spectralSequence(...,Prune=>...)
  * spectralSequencePage(...,Prune=>...)
  * spectralSequencePageMap(...,Prune=>...)

Further information
===================

  * Default value: false (Macaulay2Doc),
  * Function: spectralSequencePage, -- construct a
    spectral sequence page from a filtered complex
  * Option key: Prune (Macaulay2Doc), -- value of an optional
    argument
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:1081:0.

spectralSequencePage(FilteredComplex,ZZ) -- construct a spectral sequence page from a filtered complex
******************************************************************************************************

  * Function: spectralSequencePage,
  * Usage:
        E = spectralSequencePage(K,r)
  * Inputs:
      * K, a filtered chain complex, A filtered complex
      * r, an integer (Macaulay2Doc),
  * Optional inputs (Macaulay2Doc),:
      * Prune, =>
        ..., default value false,
  * Outputs:
      * E, a spectral sequence page,

Description
===========

Returns the rth page of the spectral sequence determined by K.

Consider the filtered complex $K$ below, obtained by multiplying the minimal
free resolution of the rational quartic space curve by successive powers of the
irrelevant ideal.

+----------------------------------------------------+
|i1 : B = QQ[a..d];                                  |
+----------------------------------------------------+
|i2 : J = ideal vars B;                              |
|                                                    |
|o2 : Ideal of B                                     |
+----------------------------------------------------+
|i3 : C = complete res monomialCurveIdeal(B,{1,3,4});|
+----------------------------------------------------+
|i4 : K = filteredComplex(J,C,4);                    |
+----------------------------------------------------+

Let $E$ be the spectral sequence determined by $K$.

+----------------------------+
|i5 : E = spectralSequence K;|
+----------------------------+

We now compute some pages.

+-----------------------------------------------------------------------------+
|i6 : E^0                                                                     |
|                                                                             |
|     +-----------------------------------------------------------------------|
|o6 = |image | a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab2d abc2|
|     |                                                                       |
|     |{-4, 4}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 3}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 2}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 1}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 0}                                                                |
|     +-----------------------------------------------------------------------|
|                                                                             |
|o6 : SpectralSequencePage                                                    |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 bd3 c4 c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|--------------------------+--------------------------------------------------|
|3d c2d2 cd3 d4 0 0 0 0 0 ||subquotient ({2} | a3 0  0  0  a2b 0   0   0   a2c|
|                          |             {3} | 0  a3 0  0  0   a2b 0   0   0  |
|                          |             {3} | 0  0  a3 0  0   0   a2b 0   0  |
|                          |             {3} | 0  0  0  a3 0   0   0   a2b 0  |
|                          |                                                  |
|                          |{-3, 4}                                           |
|--------------------------+--------------------------------------------------|
|                          |subquotient (| a3 a2b a2c a2d ab2 abc abd ac2 acd |
|                          |                                                  |
|                          |{-3, 3}                                           |
|                          |                                                  |
|                          |                                                  |
|                          |                                                  |
|--------------------------+--------------------------------------------------|
|                          |0                                                 |
|                          |                                                  |
|                          |{-3, 2}                                           |
|                          |                                                  |
|                          |                                                  |
|                          |                                                  |
|--------------------------+--------------------------------------------------|
|                          |0                                                 |
|                          |                                                  |
|                          |{-3, 1}                                           |
|                          |                                                  |
|                          |                                                  |
|                          |                                                  |
|--------------------------+--------------------------------------------------|
|                          |0                                                 |
|                          |                                                  |
|                          |{-3, 0}                                           |
|--------------------------+--------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   |
| a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   |
| 0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   |
| 0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|ad2 b3 b2c b2d bc2 bcd bd2 c3 c2d cd2 d3 a4bc-a5d a4b3-a6c a5c2-a4b2d a4c3-a4|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|ac2 0   0   0   acd 0   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b|
|0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0|
|0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0|
|0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bd2 a3b2c-a4bd a3b4-a5bc a4bc2-a3b3d a3bc3-a3b2d2 a3bc2-a4cd a3b3c-a5c2 a4c3-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2|
|   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0 |
|   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0 |
|   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a3b2cd a3c4-a3bcd2 a3bcd-a4d2 a3b3d-a5cd a4c2d-a3b2d2 a3c3d-a3bd3 a2b3c-a3b2d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d 0   0   0   cd2 0   0   0   d3 0  0  0  -a4b2 -a5c -a4bd -a4c2 -a3b3 -a4bc |
|  c2d 0   0   0   cd2 0   0   0  d3 0  0  a4c   a4d  0     0     a3bc  a3bd  |
|  0   c2d 0   0   0   cd2 0   0  0  d3 0  a5    a4b  -a4c  -a4d  a4b   a3b2  |
|  0   0   c2d 0   0   0   cd2 0  0  0  d3 0     0    a5    a4b   0     0     |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| a2b5-a4b2c a3b2c2-a2b4d a2b2c3-a2b3d2 a2b2c2-a3bcd a2b4c-a4bc2 a3bc3-a2b3cd |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-a3b2d -a3bc2 -a3b2c -a4c2 -a3bcd -a3c3 -a3b2d -a4cd -a3bd2 -a3c2d -a2b4 -a3b|
|0      0      a3c2   a3cd  0      0     a3cd   a3d2  0      0      a2b2c a2b2|
|-a3bc  -a3bd  a4c    a3bc  -a3c2  -a3cd a4d    a3bd  -a3cd  -a3d2  a3b2  a2b3|
|a4b    a3b2   0      0     a4c    a3bc  0      0     a4d    a3bd   0     0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a2bc4-a2b2cd2 a2b2cd-a3bd2 a2b4d-a4bcd a3bc2d-a2b3d2 a2bc3d-a2b2d3 a2bc3-a3c2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2c -a2b3d -a2b2c2 -a2b3c -a3bc2 -a2b2cd -a2bc3 -a2b3d -a3bcd -a2b2d2 -a2bc2d |
|d  0      0       a2bc2  a2bcd  0       0      a2bcd  a2bd2  0       0       |
|   -a2b2c -a2b2d  a3bc   a2b2c  -a2bc2  -a2bcd a3bd   a2b2d  -a2bcd  -a2bd2  |
|   a3b2   a2b3    0      0      a3bc    a2b2c  0      0      a3bd    a2b2d   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d a2b3c2-a4c3 a3c4-a2b2c2d a2c5-a2bc2d2 a2bc2d-a3cd2 a2b3cd-a4c2d a3c3d-a2b2c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-a2b2c2 -a3c3 -a2bc2d -a2c4  -a2b2cd -a3c2d -a2bcd2 -a2c3d -a2b2d2 -a3cd2 -a2|
|a2c3    a2c2d 0       0      a2c2d   a2cd2  0       0      a2cd2   a2d3   0  |
|a3c2    a2bc2 -a2c3   -a2c2d a3cd    a2bcd  -a2c2d  -a2cd2 a3d2    a2bd2  -a2|
|0       0     a3c2    a2bc2  0       0      a3cd    a2bcd  0       0      a3d|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2 a2c4d-a2bcd3 a2bcd2-a3d3 a2b3d2-a4cd2 a3c2d2-a2b2d3 a2c3d2-a2bd4 ab4c-a2b3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|bd3 -a2c2d2 -ab5 -a2b3c -ab4d -ab3c2 -ab4c -a2b2c2 -ab3cd -ab2c3 -ab4d -a2b2c|
|    0       ab3c ab3d   0     0      ab2c2 ab2cd   0      0      ab2cd ab2d2 |
|cd2 -a2d3   a2b3 ab4    -ab3c -ab3d  a2b2c ab3c    -ab2c2 -ab2cd a2b2d ab3d  |
|2   a2bd2   0    0      a2b3  ab4    0     0       a2b2c  ab3c   0     0     |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d ab6-a3b3c a2b3c2-ab5d ab3c3-ab4d2 ab3c2-a2b2cd ab5c-a3b2c2 a2b2c3-ab4cd ab2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d -ab3d2 -ab2c2d -ab3c2 -a2bc3 -ab2c2d -abc4  -ab3cd -a2bc2d -ab2cd2 -abc3d -|
|  0      0       abc3   abc2d  0       0      abc2d  abcd2   0       0      a|
|  -ab2cd -ab2d2  a2bc2  ab2c2  -abc3   -abc2d a2bcd  ab2cd   -abc2d  -abcd2 a|
|  a2b2d  ab3d    0      0      a2bc2   ab2c2  0      0       a2bcd   ab2cd  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c4-ab3cd2 ab3cd-a2b2d2 ab5d-a3b2cd a2b2c2d-ab4d2 ab2c3d-ab3d3 ab2c3-a2bc2d ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|ab3d2 -a2bcd2 -ab2d3 -abc2d2 -ab2c3 -a2c4 -abc3d -ac5  -ab2c2d -a2c3d -abc2d2|
|bcd2  abd3    0      0       ac4    ac3d  0      0     ac3d    ac2d2  0      |
|2bd2  ab2d2   -abcd2 -abd3   a2c3   abc3  -ac4   -ac3d a2c2d   abc2d  -ac3d  |
|      0       a2bd2  ab2d2   0      0     a2c3   abc3  0       0      a2c2d  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|4c2-a3bc3 a2bc4-ab3c2d abc5-ab2c2d2 ab2c2d-a2bcd2 ab4cd-a3bc2d a2bc3d-ab3cd2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| -ac4d  -ab2cd2 -a2c2d2 -abcd3 -ac3d2 -ab2d3 -a2cd3 -abd4 -ac2d3 -b6 -ab4c -b|
| 0      ac2d2   acd3    0      0      acd3   ad4    0     0      b4c b4d   0 |
| -ac2d2 a2cd2   abcd2   -ac2d2 -acd3  a2d3   abd3   -acd3 -ad4   ab4 b5    -b|
| abc2d  0       0       a2cd2  abcd2  0      0      a2d3  abd3   0   0     ab|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|abc4d-ab2cd3 ab2cd2-a2bd3 ab4d2-a3bcd2 a2bc2d2-ab3d3 abc3d2-ab2d4 abc4-a2c3d |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|5d -b4c2 -b5c -ab3c2 -b4cd -b3c3 -b5d -ab3cd -b4d2 -b3c2d -b4c2 -ab2c3 -b3c2d|
|   0     b3c2 b3cd   0     0     b3cd b3d2   0     0      b2c3  b2c2d  0     |
|4c -b4d  ab3c b4c    -b3c2 -b3cd ab3d b4d    -b3cd -b3d2  ab2c2 b3c2   -b2c3 |
|4  b5    0    0      ab3c  b4c   0    0      ab3d  b4d    0     0      ab2c2 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|ab3c3-a3c4 a2c5-ab2c3d ac6-abc3d2 abc3d-a2c2d2 ab3c2d-a3c3d a2c4d-ab2c2d2 ac5|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| -b2c4  -b4cd -ab2c2d -b3cd2 -b2c3d -b4d2 -ab2cd2 -b3d3  -b2c2d2 -b3c3 -abc4 |
| 0      b2c2d b2cd2   0      0      b2cd2 b2d3    0      0       bc4   bc3d  |
| -b2c2d ab2cd b3cd    -b2c2d -b2cd2 ab2d2 b3d2    -b2cd2 -b2d3   abc3  b2c3  |
| b3c2   0     0       ab2cd  b3cd   0     0       ab2d2  b3d2    0     0     |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d-abc2d3 abc2d2-a2cd3 ab3cd2-a3c2d2 a2c3d2-ab2cd3 ac4d2-abcd4 abcd3-a2d4 ab3d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-b2c3d -bc5  -b3c2d -abc3d -b2c2d2 -bc4d  -b3cd2 -abc2d2 -b2cd3 -bc3d2 -b3d3 |
|0      0     bc3d   bc2d2  0       0      bc2d2  bcd3    0      0      bcd3  |
|-bc4   -bc3d abc2d  b2c2d  -bc3d   -bc2d2 abcd2  b2cd2   -bc2d2 -bcd3  abd3  |
|abc3   b2c3  0      0      abc2d   b2c2d  0      0       abcd2  b2cd2  0     |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3-a3cd3 a2c2d3-ab2d4 ac3d3-abd5 b5c-ab4d b7-a2b4c ab4c2-b6d b4c3-b5d2 b4c2-ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-abcd3 -b2d4 -bc2d3 -b2c4 -ac5 -bc4d -c6  -b2c3d -ac4d -bc3d2 -c5d  -b2c2d2 -|
|bd4    0     0      c5    c4d  0     0    c4d    c3d2  0      0     c3d2    c|
|b2d3   -bcd3 -bd4   ac4   bc4  -c5   -c4d ac3d   bc3d  -c4d   -c3d2 ac2d2   b|
|0      abd3  b2d3   0     0    ac4   bc4  0      0     ac3d   bc3d  0       0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3cd b6c-a2b3c2 ab3c3-b5cd b3c4-b4cd2 b4cd-ab3d2 b6d-a2b3cd ab3c2d-b5d2 b3c3d-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|ac3d2 -bc2d3 -c4d2 -b2cd3 -ac2d3 -bcd4 -c3d3 -b2d4 -acd4 -bd5 -c2d4 a4 0  0  |
|2d3   0      0     c2d3   cd4    0     0     cd4   d5    0    0     0  a4 0  |
|c2d2  -c3d2  -c2d3 acd3   bcd3   -c2d3 -cd4  ad4   bd4   -cd4 -d5   0  0  a4 |
|      ac2d2  bc2d2 0      0      acd3  bcd3  0     0     ad4  bd4   0  0  0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b4d3 b3c3-ab2c2d b5c2-a2b2c3 ab2c4-b4c2d b2c5-b3c2d2 b3c2d-ab2cd2 b5cd-a2b2c2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0  a3b 0   0   0   a3c 0   0   0   a3d 0   0   0   a2b2 0    0    0    a2bc 0|
|0  0   a3b 0   0   0   a3c 0   0   0   a3d 0   0   0    a2b2 0    0    0    a|
|0  0   0   a3b 0   0   0   a3c 0   0   0   a3d 0   0    0    a2b2 0    0    0|
|a4 0   0   0   a3b 0   0   0   a3c 0   0   0   a3d 0    0    0    a2b2 0    0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d ab2c3d-b4cd2 b2c4d-b3cd3 b3cd2-ab2d3 b5d2-a2b2cd2 ab2c2d2-b4d3 b2c3d2-b3d4 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d|
|2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0  |
|    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0  |
|    0    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b2c4-abc3d b4c3-a2bc4 abc5-b3c3d bc6-b2c3d2 b2c3d-abc2d2 b4c2d-a2bc3d abc4d-b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2 0    0    0    ab3 0   0   0   ab2c 0    0    0    ab2d 0    0    0    abc2|
|  a2d2 0    0    0   ab3 0   0   0    ab2c 0    0    0    ab2d 0    0    0   |
|  0    a2d2 0    0   0   ab3 0   0    0    ab2c 0    0    0    ab2d 0    0   |
|  0    0    a2d2 0   0   0   ab3 0    0    0    ab2c 0    0    0    ab2d 0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3c2d2 bc5d-b2c2d3 b2c2d2-abcd3 b4cd2-a2bc2d2 abc3d2-b3cd3 bc4d2-b2cd4 b2cd3-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0    0    0    abcd 0    0    0    abd2 0    0    0    ac3 0   0   0   ac2d |
| abc2 0    0    0    abcd 0    0    0    abd2 0    0    0   ac3 0   0   0    |
| 0    abc2 0    0    0    abcd 0    0    0    abd2 0    0   0   ac3 0   0    |
| 0    0    abc2 0    0    0    abcd 0    0    0    abd2 0   0   0   ac3 0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bd4 b4d3-a2bcd3 abc2d3-b3d4 bc3d3-b2d5 bc5-ac4d b3c4-a2c5 ac6-b2c4d c7-bc4d2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0    0    0    acd2 0    0    0    ad3 0   0   0   b4 0  0  0  b3c 0   0   0 |
|ac2d 0    0    0    acd2 0    0    0   ad3 0   0   0  b4 0  0  0   b3c 0   0 |
|0    ac2d 0    0    0    acd2 0    0   0   ad3 0   0  0  b4 0  0   0   b3c 0 |
|0    0    ac2d 0    0    0    acd2 0   0   0   ad3 0  0  0  b4 0   0   0   b3|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bc4d-ac3d2 b3c3d-a2c4d ac5d-b2c3d2 c6d-bc3d3 bc3d2-ac2d3 b3c2d2-a2c3d2 ac4d2-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  b3d 0   0   0   b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0   |
|  0   b3d 0   0   0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0   |
|  0   0   b3d 0   0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0   |
|c 0   0   0   b3d 0    0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b2c2d3 c5d2-bc2d4 bc2d3-acd4 b3cd3-a2c2d3 ac3d3-b2cd4 c4d3-bcd5 bcd4-ad5 b3d4|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| bc3 0   0   0   bc2d 0    0    0    bcd2 0    0    0    bd3 0   0   0   c4 0|
| 0   bc3 0   0   0    bc2d 0    0    0    bcd2 0    0    0   bd3 0   0   0  c|
| 0   0   bc3 0   0    0    bc2d 0    0    0    bcd2 0    0   0   bd3 0   0  0|
| 0   0   0   bc3 0    0    0    bc2d 0    0    0    bcd2 0   0   0   bd3 0  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-a2cd4 ac2d4-b2d5 c3d4-bd6 a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  0  0  c3d 0   0   0   c2d2 0    0    0    cd3 0   0   0   d4 0  0  0  |, {2|
|4 0  0  0   c3d 0   0   0    c2d2 0    0    0   cd3 0   0   0  d4 0  0  |  {3|
|  c4 0  0   0   c3d 0   0    0    c2d2 0    0   0   cd3 0   0  0  d4 0  |  {3|
|  0  c4 0   0   0   c3d 0    0    0    c2d2 0   0   0   cd3 0  0  0  d4 |  {3|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b2c ab2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|} | -a4b2 -a5c -a4bd -a4c2 -a3b3 -a4bc -a3b2d -a3bc2 -a3b2c -a4c2 -a3bcd -a3c|
|} | a4c   a4d  0     0     a3bc  a3bd  0      0      a3c2   a3cd  0      0   |
|} | a5    a4b  -a4c  -a4d  a4b   a3b2  -a3bc  -a3bd  a4c    a3bc  -a3c2  -a3c|
|} | 0     0    a5    a4b   0     0     a4b    a3b2   0      0     a4c    a3bc|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bcd2 bd3 c4 c3d c2d2 cd3 d4 |, | a4bc-a5d a4b3-a6c a5c2-a4b2d a4c3-a4bd2 a3b2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|3 -a3b2d -a4cd -a3bd2 -a3c2d -a2b4 -a3b2c -a2b3d -a2b2c2 -a2b3c -a3bc2 -a2b2c|
|  a3cd   a3d2  0      0      a2b2c a2b2d  0      0       a2bc2  a2bcd  0     |
|d a4d    a3bd  -a3cd  -a3d2  a3b2  a2b3   -a2b2c -a2b2d  a3bc   a2b2c  -a2bc2|
|  0      0     a4d    a3bd   0     0      a3b2   a2b3    0      0      a3bc  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c-a4bd a3b4-a5bc a4bc2-a3b3d a3bc3-a3b2d2 a3bc2-a4cd a3b3c-a5c2 a4c3-a3b2cd a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d -a2bc3 -a2b3d -a3bcd -a2b2d2 -a2bc2d -a2b2c2 -a3c3 -a2bc2d -a2c4  -a2b2cd -|
|  0      a2bcd  a2bd2  0       0       a2c3    a2c2d 0       0      a2c2d   a|
|  -a2bcd a3bd   a2b2d  -a2bcd  -a2bd2  a3c2    a2bc2 -a2c3   -a2c2d a3cd    a|
|  a2b2c  0      0      a3bd    a2b2d   0       0     a3c2    a2bc2  0       0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3c4-a3bcd2 a3bcd-a4d2 a3b3d-a5cd a4c2d-a3b2d2 a3c3d-a3bd3 a2b3c-a3b2d a2b5-a4|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|a3c2d -a2bcd2 -a2c3d -a2b2d2 -a3cd2 -a2bd3 -a2c2d2 -ab5 -a2b3c -ab4d -ab3c2 -|
|2cd2  0       0      a2cd2   a2d3   0      0       ab3c ab3d   0     0      a|
|2bcd  -a2c2d  -a2cd2 a3d2    a2bd2  -a2cd2 -a2d3   a2b3 ab4    -ab3c -ab3d  a|
|      a3cd    a2bcd  0       0      a3d2   a2bd2   0    0      a2b3  ab4    0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b2c a3b2c2-a2b4d a2b2c3-a2b3d2 a2b2c2-a3bcd a2b4c-a4bc2 a3bc3-a2b3cd a2bc4-a2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|ab4c -a2b2c2 -ab3cd -ab2c3 -ab4d -a2b2cd -ab3d2 -ab2c2d -ab3c2 -a2bc3 -ab2c2d|
|b2c2 ab2cd   0      0      ab2cd ab2d2   0      0       abc3   abc2d  0      |
|2b2c ab3c    -ab2c2 -ab2cd a2b2d ab3d    -ab2cd -ab2d2  a2bc2  ab2c2  -abc3  |
|     0       a2b2c  ab3c   0     0       a2b2d  ab3d    0      0      a2bc2  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b2cd2 a2b2cd-a3bd2 a2b4d-a4bcd a3bc2d-a2b3d2 a2bc3d-a2b2d3 a2bc3-a3c2d a2b3c2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| -abc4  -ab3cd -a2bc2d -ab2cd2 -abc3d -ab3d2 -a2bcd2 -ab2d3 -abc2d2 -ab2c3 -a|
| 0      abc2d  abcd2   0       0      abcd2  abd3    0      0       ac4    ac|
| -abc2d a2bcd  ab2cd   -abc2d  -abcd2 a2bd2  ab2d2   -abcd2 -abd3   a2c3   ab|
| ab2c2  0      0       a2bcd   ab2cd  0      0       a2bd2  ab2d2   0      0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-a4c3 a3c4-a2b2c2d a2c5-a2bc2d2 a2bc2d-a3cd2 a2b3cd-a4c2d a3c3d-a2b2cd2 a2c4d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2c4 -abc3d -ac5  -ab2c2d -a2c3d -abc2d2 -ac4d  -ab2cd2 -a2c2d2 -abcd3 -ac3d2 |
|3d  0      0     ac3d    ac2d2  0       0      ac2d2   acd3    0      0      |
|c3  -ac4   -ac3d a2c2d   abc2d  -ac3d   -ac2d2 a2cd2   abcd2   -ac2d2 -acd3  |
|    a2c3   abc3  0       0      a2c2d   abc2d  0       0       a2cd2  abcd2  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-a2bcd3 a2bcd2-a3d3 a2b3d2-a4cd2 a3c2d2-a2b2d3 a2c3d2-a2bd4 ab4c-a2b3d ab6-a3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-ab2d3 -a2cd3 -abd4 -ac2d3 -b6 -ab4c -b5d -b4c2 -b5c -ab3c2 -b4cd -b3c3 -b5d |
|acd3   ad4    0     0      b4c b4d   0    0     b3c2 b3cd   0     0     b3cd |
|a2d3   abd3   -acd3 -ad4   ab4 b5    -b4c -b4d  ab3c b4c    -b3c2 -b3cd ab3d |
|0      0      a2d3  abd3   0   0     ab4  b5    0    0      ab3c  b4c   0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b3c a2b3c2-ab5d ab3c3-ab4d2 ab3c2-a2b2cd ab5c-a3b2c2 a2b2c3-ab4cd ab2c4-ab3cd|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-ab3cd -b4d2 -b3c2d -b4c2 -ab2c3 -b3c2d -b2c4  -b4cd -ab2c2d -b3cd2 -b2c3d -b|
|b3d2   0     0      b2c3  b2c2d  0      0      b2c2d b2cd2   0      0      b2|
|b4d    -b3cd -b3d2  ab2c2 b3c2   -b2c3  -b2c2d ab2cd b3cd    -b2c2d -b2cd2 ab|
|0      ab3d  b4d    0     0      ab2c2  b3c2   0     0       ab2cd  b3cd   0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2 ab3cd-a2b2d2 ab5d-a3b2cd a2b2c2d-ab4d2 ab2c3d-ab3d3 ab2c3-a2bc2d ab4c2-a3bc|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|4d2 -ab2cd2 -b3d3  -b2c2d2 -b3c3 -abc4 -b2c3d -bc5  -b3c2d -abc3d -b2c2d2 -bc|
|cd2 b2d3    0      0       bc4   bc3d  0      0     bc3d   bc2d2  0       0  |
|2d2 b3d2    -b2cd2 -b2d3   abc3  b2c3  -bc4   -bc3d abc2d  b2c2d  -bc3d   -bc|
|    0       ab2d2  b3d2    0     0     abc3   b2c3  0      0      abc2d   b2c|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3 a2bc4-ab3c2d abc5-ab2c2d2 ab2c2d-a2bcd2 ab4cd-a3bc2d a2bc3d-ab3cd2 abc4d-ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|4d  -b3cd2 -abc2d2 -b2cd3 -bc3d2 -b3d3 -abcd3 -b2d4 -bc2d3 -b2c4 -ac5 -bc4d -|
|    bc2d2  bcd3    0      0      bcd3  bd4    0     0      c5    c4d  0     0|
|2d2 abcd2  b2cd2   -bc2d2 -bcd3  abd3  b2d3   -bcd3 -bd4   ac4   bc4  -c5   -|
|2d  0      0       abcd2  b2cd2  0     0      abd3  b2d3   0     0    ac4   b|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2cd3 ab2cd2-a2bd3 ab4d2-a3bcd2 a2bc2d2-ab3d3 abc3d2-ab2d4 abc4-a2c3d ab3c3-a3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c6  -b2c3d -ac4d -bc3d2 -c5d  -b2c2d2 -ac3d2 -bc2d3 -c4d2 -b2cd3 -ac2d3 -bcd4|
|    c4d    c3d2  0      0     c3d2    c2d3   0      0     c2d3   cd4    0    |
|c4d ac3d   bc3d  -c4d   -c3d2 ac2d2   bc2d2  -c3d2  -c2d3 acd3   bcd3   -c2d3|
|c4  0      0     ac3d   bc3d  0       0      ac2d2  bc2d2 0      0      acd3 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c4 a2c5-ab2c3d ac6-abc3d2 abc3d-a2c2d2 ab3c2d-a3c3d a2c4d-ab2c2d2 ac5d-abc2d3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| -c3d3 -b2d4 -acd4 -bd5 -c2d4 a4 0  0  0  a3b 0   0   0   a3c 0   0   0   a3d|
| 0     cd4   d5    0    0     0  a4 0  0  0   a3b 0   0   0   a3c 0   0   0  |
| -cd4  ad4   bd4   -cd4 -d5   0  0  a4 0  0   0   a3b 0   0   0   a3c 0   0  |
| bcd3  0     0     ad4  bd4   0  0  0  a4 0   0   0   a3b 0   0   0   a3c 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| abc2d2-a2cd3 ab3cd2-a3c2d2 a2c3d2-ab2cd3 ac4d2-abcd4 abcd3-a2d4 ab3d3-a3cd3 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   0   0   a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    a2c2|
| a3d 0   0   0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0   |
| 0   a3d 0   0    0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0   |
| 0   0   a3d 0    0    0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a2c2d3-ab2d4 ac3d3-abd5 b5c-ab4d b7-a2b4c ab4c2-b6d b4c3-b5d2 b4c2-ab3cd b6c-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0    0    0    a2cd 0    0    0    a2d2 0    0    0    ab3 0   0   0   ab2c |
| a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0    0   ab3 0   0   0    |
| 0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0   0   ab3 0   0    |
| 0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0   0   0   ab3 0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a2b3c2 ab3c3-b5cd b3c4-b4cd2 b4cd-ab3d2 b6d-a2b3cd ab3c2d-b5d2 b3c3d-b4d3 b3c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0    ab|
|ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0 |
|0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0 |
|0    0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3-ab2c2d b5c2-a2b2c3 ab2c4-b4c2d b2c5-b3c2d2 b3c2d-ab2cd2 b5cd-a2b2c2d ab2c3d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d2 0    0    0    ac3 0   0   0   ac2d 0    0    0    acd2 0    0    0    ad3|
|   abd2 0    0    0   ac3 0   0   0    ac2d 0    0    0    acd2 0    0    0  |
|   0    abd2 0    0   0   ac3 0   0    0    ac2d 0    0    0    acd2 0    0  |
|   0    0    abd2 0   0   0   ac3 0    0    0    ac2d 0    0    0    acd2 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-b4cd2 b2c4d-b3cd3 b3cd2-ab2d3 b5d2-a2b2cd2 ab2c2d2-b4d3 b2c3d2-b3d4 b2c4-abc|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   0   0   b4 0  0  0  b3c 0   0   0   b3d 0   0   0   b2c2 0    0    0    |
| ad3 0   0   0  b4 0  0  0   b3c 0   0   0   b3d 0   0   0    b2c2 0    0    |
| 0   ad3 0   0  0  b4 0  0   0   b3c 0   0   0   b3d 0   0    0    b2c2 0    |
| 0   0   ad3 0  0  0  b4 0   0   0   b3c 0   0   0   b3d 0    0    0    b2c2 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3d b4c3-a2bc4 abc5-b3c3d bc6-b2c3d2 b2c3d-abc2d2 b4c2d-a2bc3d abc4d-b3c2d2 bc|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|b2cd 0    0    0    b2d2 0    0    0    bc3 0   0   0   bc2d 0    0    0    b|
|0    b2cd 0    0    0    b2d2 0    0    0   bc3 0   0   0    bc2d 0    0    0|
|0    0    b2cd 0    0    0    b2d2 0    0   0   bc3 0   0    0    bc2d 0    0|
|0    0    0    b2cd 0    0    0    b2d2 0   0   0   bc3 0    0    0    bc2d 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|5d-b2c2d3 b2c2d2-abcd3 b4cd2-a2bc2d2 abc3d2-b3cd3 bc4d2-b2cd4 b2cd3-abd4 b4d3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|cd2 0    0    0    bd3 0   0   0   c4 0  0  0  c3d 0   0   0   c2d2 0    0   |
|    bcd2 0    0    0   bd3 0   0   0  c4 0  0  0   c3d 0   0   0    c2d2 0   |
|    0    bcd2 0    0   0   bd3 0   0  0  c4 0  0   0   c3d 0   0    0    c2d2|
|    0    0    bcd2 0   0   0   bd3 0  0  0  c4 0   0   0   c3d 0    0    0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-a2bcd3 abc2d3-b3d4 bc3d3-b2d5 bc5-ac4d b3c4-a2c5 ac6-b2c4d c7-bc4d2 bc4d-ac3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0    cd3 0   0   0   d4 0  0  0  |)                                         |
| 0    0   cd3 0   0   0  d4 0  0  |                                          |
| 0    0   0   cd3 0   0  0  d4 0  |                                          |
| c2d2 0   0   0   cd3 0  0  0  d4 |                                          |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2 b3c3d-a2c4d ac5d-b2c3d2 c6d-bc3d3 bc3d2-ac2d3 b3c2d2-a2c3d2 ac4d2-b2c2d3 c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|5d2-bc2d4 bc2d3-acd4 b3cd3-a2c2d3 ac3d3-b2cd4 c4d3-bcd5 bcd4-ad5 b3d4-a2cd4 a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2d4-b2d5 c3d4-bd6 a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab2d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 bd3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|----------------------+------------------------------------------------------|
|                      |subquotient ({4} | a2 0  0  0  ab 0  0  0  ac 0  0  0 |
|                      |             {4} | 0  a2 0  0  0  ab 0  0  0  ac 0  0 |
|                      |             {4} | 0  0  a2 0  0  0  ab 0  0  0  ac 0 |
|                      |             {4} | 0  0  0  a2 0  0  0  ab 0  0  0  ac|
|                      |                                                      |
|                      |{-2, 4}                                               |
|----------------------+------------------------------------------------------|
| c4 c3d c2d2 cd3 d4 |)|subquotient ({2} | a2 0  0  0  ab 0  0  0  ac 0  0  0 |
|                      |             {3} | 0  a2 0  0  0  ab 0  0  0  ac 0  0 |
|                      |             {3} | 0  0  a2 0  0  0  ab 0  0  0  ac 0 |
|                      |             {3} | 0  0  0  a2 0  0  0  ab 0  0  0  ac|
|                      |                                                      |
|                      |{-2, 3}                                               |
|----------------------+------------------------------------------------------|
|                      |subquotient (| a2 ab ac ad b2 bc bd c2 cd d2 a3bc-a4d |
|                      |                                                      |
|                      |{-2, 2}                                               |
|                      |                                                      |
|                      |                                                      |
|                      |                                                      |
|----------------------+------------------------------------------------------|
|                      |0                                                     |
|                      |                                                      |
|                      |{-2, 1}                                               |
|                      |                                                      |
|                      |                                                      |
|                      |                                                      |
|----------------------+------------------------------------------------------|
|                      |0                                                     |
|                      |                                                      |
|                      |{-2, 0}                                               |
|----------------------+------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0|
| 0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d|
| 0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0|
| 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0|
| 0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d|
| 0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0|
| 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a3b3-a5c a4c2-a3b2d a3c3-a3bd2 a2b2c-a3bd a2b4-a4bc a3bc2-a2b3d a2bc3-a2b2d2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  0  0  a3d  a2bd  a2cd  a2d2  ab2d  abcd  abd2  ac2d  acd2  ad3   b3d  b2cd |
|2 0  0  -a3c -a2bc -a2c2 -a2cd -ab2c -abc2 -abcd -ac3  -ac2d -acd2 -b3c -b2c2|
|  d2 0  -a3b -a2b2 -a2bc -a2bd -ab3  -ab2c -ab2d -abc2 -abcd -abd2 -b4  -b3c |
|  0  d2 a4   a3b   a3c   a3d   a2b2  a2bc  a2bd  a2c2  a2cd  a2d2  ab3  ab2c |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  0  0  -a3b2 -a4c -a3bd -a3c2 -a2b3 -a3bc -a2b2d -a2bc2 -a2b2c -a3c2 -a2bcd |
|2 0  0  a3c   a3d  0     0     a2bc  a2bd  0      0      a2c2   a2cd  0      |
|  d2 0  a4    a3b  -a3c  -a3d  a3b   a2b2  -a2bc  -a2bd  a3c    a2bc  -a2c2  |
|  0  d2 0     0    a4    a3b   0     0     a3b    a2b2   0      0     a3c    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a2bc2-a3cd a2b3c-a4c2 a3c3-a2b2cd a2c4-a2bcd2 a2bcd-a3d2 a2b3d-a4cd a3c2d-a2b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| b2d2  bc2d  bcd2  bd3   c3d  c2d2  cd3   d4   a3 0  0  0  a2b 0   0   0   a2|
| -b2cd -bc3  -bc2d -bcd2 -c4  -c3d  -c2d2 -cd3 0  a3 0  0  0   a2b 0   0   0 |
| -b3d  -b2c2 -b2cd -b2d2 -bc3 -bc2d -bcd2 -bd3 0  0  a3 0  0   0   a2b 0   0 |
| ab2d  abc2  abcd  abd2  ac3  ac2d  acd2  ad3  0  0  0  a3 0   0   0   a2b 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-a2c3 -a2b2d -a3cd -a2bd2 -a2c2d -ab4 -a2b2c -ab3d -ab2c2 -ab3c -a2bc2 -ab2cd|
|0     a2cd   a2d2  0      0      ab2c ab2d   0     0      abc2  abcd   0     |
|-a2cd a3d    a2bd  -a2cd  -a2d2  a2b2 ab3    -ab2c -ab2d  a2bc  ab2c   -abc2 |
|a2bc  0      0     a3d    a2bd   0    0      a2b2  ab3    0     0      a2bc  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2d2 a2c3d-a2bd3 ab3c-a2b2d ab5-a3b2c a2b2c2-ab4d ab2c3-ab3d2 ab2c2-a2bcd ab4c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0  |
|  a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0  |
|  0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0  |
|  0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| -abc3 -ab3d -a2bcd -ab2d2 -abc2d -ab2c2 -a2c3 -abc2d -ac4  -ab2cd -a2c2d -ab|
| 0     abcd  abd2   0      0      ac3    ac2d  0      0     ac2d   acd2   0  |
| -abcd a2bd  ab2d   -abcd  -abd2  a2c2   abc2  -ac3   -ac2d a2cd   abcd   -ac|
| ab2c  0     0      a2bd   ab2d   0      0     a2c2   abc2  0      0      a2c|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-a3bc2 a2bc3-ab3cd abc4-ab2cd2 ab2cd-a2bd2 ab4d-a3bcd a2bc2d-ab3d2 abc3d-ab2d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| ac2 0   0   0   acd 0   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   |
| 0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   |
| 0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   |
| 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|cd2 -ac3d -ab2d2 -a2cd2 -abd3 -ac2d2 -b5 -ab3c -b4d -b3c2 -b4c -ab2c2 -b3cd -|
|    0     acd2   ad3    0     0      b3c b3d   0    0     b2c2 b2cd   0     0|
|2d  -acd2 a2d2   abd2   -acd2 -ad3   ab3 b4    -b3c -b3d  ab2c b3c    -b2c2 -|
|d   abcd  0      0      a2d2  abd2   0   0     ab3  b4    0    0      ab2c  b|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3 abc3-a2c2d ab3c2-a3c3 a2c4-ab2c2d ac5-abc2d2 abc2d-a2cd2 ab3cd-a3c2d a2c3d-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c|
|0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0|
|0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0|
|0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b2c3 -b4d -ab2cd -b3d2 -b2c2d -b3c2 -abc3 -b2c2d -bc4  -b3cd -abc2d -b2cd2 -b|
|     b2cd b2d2   0     0      bc3   bc2d  0      0     bc2d  bcd2   0      0 |
|b2cd ab2d b3d    -b2cd -b2d2  abc2  b2c2  -bc3   -bc2d abcd  b2cd   -bc2d  -b|
|3c   0    0      ab2d  b3d    0     0     abc2   b2c2  0     0      abcd   b2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|ab2cd2 ac4d-abcd3 abcd2-a2d3 ab3d2-a3cd2 a2c2d2-ab2d3 ac3d2-abd4 b4c-ab3d b6-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2d 0   0   0   cd2 0   0   0   d3 0  0  0  |, {4} | a3d  a2bd  a2cd  a2d2  ab|
|   c2d 0   0   0   cd2 0   0   0  d3 0  0  |  {4} | -a3c -a2bc -a2c2 -a2cd -a|
|   0   c2d 0   0   0   cd2 0   0  0  d3 0  |  {4} | -a3b -a2b2 -a2bc -a2bd -a|
|   0   0   c2d 0   0   0   cd2 0  0  0  d3 |  {4} | a4   a3b   a3c   a3d   a2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c3d -b3d2 -abcd2 -b2d3 -bc2d2 -b2c3 -ac4 -bc3d -c5  -b2c2d -ac3d -bc2d2 -c4d |
|    bcd2  bd3    0     0      c4    c3d  0     0    c3d    c2d2  0      0    |
|cd2 abd2  b2d2   -bcd2 -bd3   ac3   bc3  -c4   -c3d ac2d   bc2d  -c3d   -c2d2|
|cd  0     0      abd2  b2d2   0     0    ac3   bc3  0      0     ac2d   bc2d |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a2b3c ab3c2-b5d b3c3-b4d2 b3c2-ab2cd b5c-a2b2c2 ab2c3-b4cd b2c4-b3cd2 b3cd-ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2d  abcd  abd2  ac2d  acd2  ad3   b3d  b2cd  b2d2  bc2d  bcd2  bd3   c3d  c2d|
|b2c -abc2 -abcd -ac3  -ac2d -acd2 -b3c -b2c2 -b2cd -bc3  -bc2d -bcd2 -c4  -c3|
|b3  -ab2c -ab2d -abc2 -abcd -abd2 -b4  -b3c  -b3d  -b2c2 -b2cd -b2d2 -bc3 -bc|
|b2  a2bc  a2bd  a2c2  a2cd  a2d2  ab3  ab2c  ab2d  abc2  abcd  abd2  ac3  ac2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| -b2cd2 -ac2d2 -bcd3 -c3d2 -b2d3 -acd3 -bd4 -c2d3 a3 0  0  0  a2b 0   0   0  |
| c2d2   cd3    0     0     cd3   d4    0    0     0  a3 0  0  0   a2b 0   0  |
| acd2   bcd2   -c2d2 -cd3  ad3   bd3   -cd3 -d4   0  0  a3 0  0   0   a2b 0  |
| 0      0      acd2  bcd2  0     0     ad3  bd3   0  0  0  a3 0   0   0   a2b|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2d2 b5d-a2b2cd ab2c2d-b4d2 b2c3d-b3d3 b2c3-abc2d b4c2-a2bc3 abc4-b3c2d bc5-b2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2  cd3   d4   a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2|
|d  -c2d2 -cd3 0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0  |
|2d -bcd2 -bd3 0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0  |
|d  acd2  ad3  0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   a2d 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   |
| 0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   |
| 0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd |
| 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2d2 b2c2d-abcd2 b4cd-a2bc2d abc3d-b3cd2 bc4d-b2cd3 b2cd2-abd3 b4d2-a2bcd2 ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   |
| ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   |
| 0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   |
| 0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0|
|0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0|
|0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0|
|abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2d2-b3d3 bc3d2-b2d4 bc4-ac3d b3c3-a2c4 ac5-b2c3d c6-bc3d2 bc3d-ac2d2 b3c2d-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   b|
|0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0|
|0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0|
|0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0   bc2 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0|
|   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0|
|   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0|
|2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2c3d ac4d-b2c2d2 c5d-bc2d3 bc2d2-acd3 b3cd2-a2c2d2 ac3d2-b2cd3 c4d2-bcd4 bcd3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|cd 0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0   0   d3|
|   bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0   0   0 |
|   0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2 0   0 |
|   0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0   cd2 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  c2d 0   0   0   cd2 0   0   0   d3 0  0  0  |, {2} | -a3b2 -a4c -a3bd -a3c2|
|  0   c2d 0   0   0   cd2 0   0   0  d3 0  0  |  {3} | a3c   a3d  0     0    |
|  0   0   c2d 0   0   0   cd2 0   0  0  d3 0  |  {3} | a4    a3b  -a3c  -a3d |
|3 0   0   0   c2d 0   0   0   cd2 0  0  0  d3 |  {3} | 0     0    a4    a3b  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-ad4 b3d3-a2cd3 ac2d3-b2d4 c3d3-bd5 a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0  0  0  |)                                                                 |
| d3 0  0  |                                                                  |
| 0  d3 0  |                                                                  |
| 0  0  d3 |                                                                  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| -a2b3 -a3bc -a2b2d -a2bc2 -a2b2c -a3c2 -a2bcd -a2c3 -a2b2d -a3cd -a2bd2 -a2c|
| a2bc  a2bd  0      0      a2c2   a2cd  0      0     a2cd   a2d2  0      0   |
| a3b   a2b2  -a2bc  -a2bd  a3c    a2bc  -a2c2  -a2cd a3d    a2bd  -a2cd  -a2d|
| 0     0     a3b    a2b2   0      0     a3c    a2bc  0      0     a3d    a2bd|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| b2c b2d bc2 bcd bd2 c3 c2d cd2 d3 |, | a3bc-a4d a3b3-a5c a4c2-a3b2d a3c3-a3b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2d -ab4 -a2b2c -ab3d -ab2c2 -ab3c -a2bc2 -ab2cd -abc3 -ab3d -a2bcd -ab2d2 -ab|
|   ab2c ab2d   0     0      abc2  abcd   0      0     abcd  abd2   0      0  |
|2  a2b2 ab3    -ab2c -ab2d  a2bc  ab2c   -abc2  -abcd a2bd  ab2d   -abcd  -ab|
|   0    0      a2b2  ab3    0     0      a2bc   ab2c  0     0      a2bd   ab2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2 a2b2c-a3bd a2b4-a4bc a3bc2-a2b3d a2bc3-a2b2d2 a2bc2-a3cd a2b3c-a4c2 a3c3-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2d -ab2c2 -a2c3 -abc2d -ac4  -ab2cd -a2c2d -abcd2 -ac3d -ab2d2 -a2cd2 -abd3 |
|    ac3    ac2d  0      0     ac2d   acd2   0      0     acd2   ad3    0     |
|d2  a2c2   abc2  -ac3   -ac2d a2cd   abcd   -ac2d  -acd2 a2d2   abd2   -acd2 |
|d   0      0     a2c2   abc2  0      0      a2cd   abcd  0      0      a2d2  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2b2cd a2c4-a2bcd2 a2bcd-a3d2 a2b3d-a4cd a3c2d-a2b2d2 a2c3d-a2bd3 ab3c-a2b2d a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-ac2d2 -b5 -ab3c -b4d -b3c2 -b4c -ab2c2 -b3cd -b2c3 -b4d -ab2cd -b3d2 -b2c2d |
|0      b3c b3d   0    0     b2c2 b2cd   0     0     b2cd b2d2   0     0      |
|-ad3   ab3 b4    -b3c -b3d  ab2c b3c    -b2c2 -b2cd ab2d b3d    -b2cd -b2d2  |
|abd2   0   0     ab3  b4    0    0      ab2c  b3c   0    0      ab2d  b3d    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b5-a3b2c a2b2c2-ab4d ab2c3-ab3d2 ab2c2-a2bcd ab4c-a3bc2 a2bc3-ab3cd abc4-ab2c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-b3c2 -abc3 -b2c2d -bc4  -b3cd -abc2d -b2cd2 -bc3d -b3d2 -abcd2 -b2d3 -bc2d2 |
|bc3   bc2d  0      0     bc2d  bcd2   0      0     bcd2  bd3    0     0      |
|abc2  b2c2  -bc3   -bc2d abcd  b2cd   -bc2d  -bcd2 abd2  b2d2   -bcd2 -bd3   |
|0     0     abc2   b2c2  0     0      abcd   b2cd  0     0      abd2  b2d2   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2 ab2cd-a2bd2 ab4d-a3bcd a2bc2d-ab3d2 abc3d-ab2d3 abc3-a2c2d ab3c2-a3c3 a2c4|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-b2c3 -ac4 -bc3d -c5  -b2c2d -ac3d -bc2d2 -c4d  -b2cd2 -ac2d2 -bcd3 -c3d2 -b2|
|c4    c3d  0     0    c3d    c2d2  0      0     c2d2   cd3    0     0     cd3|
|ac3   bc3  -c4   -c3d ac2d   bc2d  -c3d   -c2d2 acd2   bcd2   -c2d2 -cd3  ad3|
|0     0    ac3   bc3  0      0     ac2d   bc2d  0      0      acd2  bcd2  0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-ab2c2d ac5-abc2d2 abc2d-a2cd2 ab3cd-a3c2d a2c3d-ab2cd2 ac4d-abcd3 abcd2-a2d3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d3 -acd3 -bd4 -c2d3 a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   0|
|   d4    0    0     0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   0|
|   bd3   -cd3 -d4   0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d 0|
|   0     ad3  bd3   0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   a|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| ab3d2-a3cd2 a2c2d2-ab2d3 ac3d2-abd4 b4c-ab3d b6-a2b3c ab3c2-b5d b3c3-b4d2 b3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0 |
|   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0 |
|   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   ac|
|2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2-ab2cd b5c-a2b2c2 ab2c3-b4cd b2c4-b3cd2 b3cd-ab2d2 b5d-a2b2cd ab2c2d-b4d2 b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0  |
|  0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0  |
|d 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc2|
|  acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2c3d-b3d3 b2c3-abc2d b4c2-a2bc3 abc4-b3c2d bc5-b2c2d2 b2c2d-abcd2 b4cd-a2bc2d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0   |
| 0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0   |
| 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2 |
| bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| abc3d-b3cd2 bc4d-b2cd3 b2cd2-abd3 b4d2-a2bcd2 abc2d2-b3d3 bc3d2-b2d4 bc4-ac3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|0   d3 0  0  0  |)                                                           |
|0   0  d3 0  0  |                                                            |
|0   0  0  d3 0  |                                                            |
|cd2 0  0  0  d3 |                                                            |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d b3c3-a2c4 ac5-b2c3d c6-bc3d2 bc3d-ac2d2 b3c2d-a2c3d ac4d-b2c2d2 c5d-bc2d3 b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2d2-acd3 b3cd2-a2c2d2 ac3d2-b2cd3 c4d2-bcd4 bcd3-ad4 b3d3-a2cd3 ac2d3-b2d4 c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3d3-bd5 a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3 b2c b2d bc2 bcd bd2 c3 c2d |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|---------+-------------------------------------------------------------------|
|         |subquotient ({5} | a b c d a2 ab ac ad b2 bc bd c2 cd d2 |, {5} | a|
|         |                                                                   |
|         |{-1, 4}                                                            |
|         |                                                                   |
|         |                                                                   |
|         |                                                                   |
|---------+-------------------------------------------------------------------|
|         |subquotient ({4} | a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 a2d  abd  acd  a|
|         |             {4} | 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 -a2c -abc -ac2 -|
|         |             {4} | 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 -a2b -ab2 -abc -|
|         |             {4} | 0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d a3   a2b  a2c  a|
|         |                                                                   |
|         |{-1, 3}                                                            |
|---------+-------------------------------------------------------------------|
|cd2 d3 |)|subquotient ({2} | a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 -a2b2 -a3c -a2bd|
|         |             {3} | 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 a2c   a2d  0    |
|         |             {3} | 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 a3    a2b  -a2c |
|         |             {3} | 0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0     0    a3   |
|         |                                                                   |
|         |{-1, 2}                                                            |
|---------+-------------------------------------------------------------------|
|         |subquotient (| a b c d a2bc-a3d a2b3-a4c a3c2-a2b2d a2c3-a2bd2 ab2c|
|         |                                                                   |
|         |{-1, 1}                                                            |
|         |                                                                   |
|         |                                                                   |
|         |                                                                   |
|---------+-------------------------------------------------------------------|
|         |0                                                                  |
|         |                                                                   |
|         |{-1, 0}                                                            |
|---------+-------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2 ab ac ad b2 bc bd c2 cd d2 |)                                              |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2  b2d  bcd  bd2  c2d  cd2  d3   a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0|
|acd -b2c -bc2 -bcd -c3  -c2d -cd2 0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0|
|abd -b3  -b2c -b2d -bc2 -bcd -bd2 0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  a|
|2d  ab2  abc  abd  ac2  acd  ad2  0  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| -a2c2 -ab3 -a2bc -ab2d -abc2 -ab2c -a2c2 -abcd -ac3 -ab2d -a2cd -abd2 -ac2d |
| 0     abc  abd   0     0     ac2   acd   0     0    acd   ad2   0     0     |
| -a2d  a2b  ab2   -abc  -abd  a2c   abc   -ac2  -acd a2d   abd   -acd  -ad2  |
| a2b   0    0     a2b   ab2   0     0     a2c   abc  0     0     a2d   abd   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-a2bd ab4-a3bc a2bc2-ab3d abc3-ab2d2 abc2-a2cd ab3c-a3c2 a2c3-ab2cd ac4-abcd2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |
|  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |
|d 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |
|  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-b4 -ab2c -b3d -b2c2 -b3c -abc2 -b2cd -bc3 -b3d -abcd -b2d2 -bc2d -b2c2 -ac3 |
|b2c b2d   0    0     bc2  bcd   0     0    bcd  bd2   0     0     c3    c2d  |
|ab2 b3    -b2c -b2d  abc  b2c   -bc2  -bcd abd  b2d   -bcd  -bd2  ac2   bc2  |
|0   0     ab2  b3    0    0     abc   b2c  0    0     abd   b2d   0     0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| abcd-a2d2 ab3d-a3cd a2c2d-ab2d2 ac3d-abd3 b3c-ab2d b5-a2b2c ab2c2-b4d b2c3-b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
||, {4} | a2d  abd  acd  ad2  b2d  bcd  bd2  c2d  cd2  d3   a2 0  0  0  ab 0  |
||  {4} | -a2c -abc -ac2 -acd -b2c -bc2 -bcd -c3  -c2d -cd2 0  a2 0  0  0  ab |
||  {4} | -a2b -ab2 -abc -abd -b3  -b2c -b2d -bc2 -bcd -bd2 0  0  a2 0  0  0  |
||  {4} | a3   a2b  a2c  a2d  ab2  abc  abd  ac2  acd  ad2  0  0  0  a2 0  0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-bc2d -c4  -b2cd -ac2d -bcd2 -c3d -b2d2 -acd2 -bd3 -c2d2 a2 0  0  0  ab 0  0 |
|0     0    c2d   cd2   0     0    cd2   d3    0    0     0  a2 0  0  0  ab 0 |
|-c3   -c2d acd   bcd   -c2d  -cd2 ad2   bd2   -cd2 -d3   0  0  a2 0  0  0  ab|
|ac2   bc2  0     0     acd   bcd  0     0     ad2  bd2   0  0  0  a2 0  0  0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3d2 b2c2-abcd b4c-a2bc2 abc3-b3cd bc4-b2cd2 b2cd-abd2 b4d-a2bcd abc2d-b3d2 bc|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0 |
|0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0 |
|ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0 |
|0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  c|
| 0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0|
| 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0|
| ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3d-b2d3 bc3-ac2d b3c2-a2c3 ac4-b2c2d c5-bc2d2 bc2d-acd2 b3cd-a2c2d ac3d-b2cd2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| cd 0  0  0  d2 0  0  0  |)                                                  |
| 0  cd 0  0  0  d2 0  0  |                                                   |
| 0  0  cd 0  0  0  d2 0  |                                                   |
| 0  0  0  cd 0  0  0  d2 |                                                   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d 0  0  0  d2 0  0  0  |, {2} | -a2b2 -a3c -a2bd -a2c2 -ab3 -a2bc -ab2d -abc2|
|  cd 0  0  0  d2 0  0  |  {3} | a2c   a2d  0     0     abc  abd   0     0    |
|  0  cd 0  0  0  d2 0  |  {3} | a3    a2b  -a2c  -a2d  a2b  ab2   -abc  -abd |
|  0  0  cd 0  0  0  d2 |  {3} | 0     0    a3    a2b   0    0     a2b   ab2  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| c4d-bcd3 bcd2-ad3 b3d2-a2cd2 ac2d2-b2d3 c3d2-bd4 a2 ab ac ad b2 bc bd c2 cd |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| -ab2c -a2c2 -abcd -ac3 -ab2d -a2cd -abd2 -ac2d -b4 -ab2c -b3d -b2c2 -b3c -ab|
| ac2   acd   0     0    acd   ad2   0     0     b2c b2d   0    0     bc2  bcd|
| a2c   abc   -ac2  -acd a2d   abd   -acd  -ad2  ab2 b3    -b2c -b2d  abc  b2c|
| 0     0     a2c   abc  0     0     a2d   abd   0   0     ab2  b3    0    0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2 |, | a2bc-a3d a2b3-a4c a3c2-a2b2d a2c3-a2bd2 ab2c-a2bd ab4-a3bc a2bc2-ab3d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2 -b2cd -bc3 -b3d -abcd -b2d2 -bc2d -b2c2 -ac3 -bc2d -c4  -b2cd -ac2d -bcd2 |
|   0     0    bcd  bd2   0     0     c3    c2d  0     0    c2d   cd2   0     |
|   -bc2  -bcd abd  b2d   -bcd  -bd2  ac2   bc2  -c3   -c2d acd   bcd   -c2d  |
|   abc   b2c  0    0     abd   b2d   0     0    ac2   bc2  0     0     acd   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| abc3-ab2d2 abc2-a2cd ab3c-a3c2 a2c3-ab2cd ac4-abcd2 abcd-a2d2 ab3d-a3cd a2c2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-c3d -b2d2 -acd2 -bd3 -c2d2 a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b|
|0    cd2   d3    0    0     0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0|
|-cd2 ad2   bd2   -cd2 -d3   0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0|
|bcd  0     0     ad2  bd2   0  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d-ab2d2 ac3d-abd3 b3c-ab2d b5-a2b2c ab2c2-b4d b2c3-b3d2 b2c2-abcd b4c-a2bc2 a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |)    |
|  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |     |
|  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |     |
|  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |     |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bc3-b3cd bc4-b2cd2 b2cd-abd2 b4d-a2bcd abc2d-b3d2 bc3d-b2d3 bc3-ac2d b3c2-a2c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3 ac4-b2c2d c5-bc2d2 bc2d-acd2 b3cd-a2c2d ac3d-b2cd2 c4d-bcd3 bcd2-ad3 b3d2-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|---------------------------------------------------------+-------------------|
|                                                         |0                  |
|                                                         |                   |
|                                                         |{0, 4}             |
|                                                         |                   |
|                                                         |                   |
|                                                         |                   |
|---------------------------------------------------------+-------------------|
|                                                         |cokernel {5} | a b |
|                                                         |                   |
|                                                         |{0, 3}             |
|                                                         |                   |
|                                                         |                   |
|                                                         |                   |
|---------------------------------------------------------+-------------------|
|                                                         |cokernel {4} | ad  |
|                                                         |         {4} | -ac |
|                                                         |         {4} | -ab |
|                                                         |         {4} | a2  |
|                                                         |                   |
|                                                         |{0, 2}             |
|---------------------------------------------------------+-------------------|
|2cd2 ac2d2-b2d3 c3d2-bd4 a2 ab ac ad b2 bc bd c2 cd d2 |)|cokernel {2} | -ab2|
|                                                         |         {3} | ac  |
|                                                         |         {3} | a2  |
|                                                         |         {3} | 0   |
|                                                         |                   |
|                                                         |{0, 1}             |
|---------------------------------------------------------+-------------------|
|                                                         |cokernel | abc-a2d |
|                                                         |                   |
|                                                         |{0, 0}             |
|---------------------------------------------------------+-------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c d |                                                                        |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bd  cd  d2  a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 |                                |
|-bc -c2 -cd 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 |                                |
|-b2 -bc -bd 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 |                                |
|ab  ac  ad  0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d |                                |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| -a2c -abd -ac2 -b3 -abc -b2d -bc2 -b2c -ac2 -bcd -c3 -b2d -acd -bd2 -c2d a 0|
| ad   0    0    bc  bd   0    0    c2   cd   0    0   cd   d2   0    0    0 a|
| ab   -ac  -ad  ab  b2   -bc  -bd  ac   bc   -c2  -cd ad   bd   -cd  -d2  0 0|
| 0    a2   ab   0   0    ab   b2   0    0    ac   bc  0    0    ad   bd   0 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|ab3-a3c a2c2-ab2d ac3-abd2 b2c-abd b4-a2bc abc2-b3d bc3-b2d2 bc2-acd b3c-a2c2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|--------------------------------------------------------------+              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|--------------------------------------------------------------+              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|--------------------------------------------------------------+              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|                                                              |              |
|--------------------------------------------------------------+              |
| 0 0 b 0 0 0 c 0 0 0 d 0 0 0 |                                |              |
| 0 0 0 b 0 0 0 c 0 0 0 d 0 0 |                                |              |
| a 0 0 0 b 0 0 0 c 0 0 0 d 0 |                                |              |
| 0 a 0 0 0 b 0 0 0 c 0 0 0 d |                                |              |
|                                                              |              |
|                                                              |              |
|--------------------------------------------------------------+              |
| ac3-b2cd c4-bcd2 bcd-ad2 b3d-a2cd ac2d-b2d2 c3d-bd3 a b c d ||              |
|                                                              |              |
|                                                              |              |
|--------------------------------------------------------------+              |
+-----------------------------------------------------------------------------+
|i7 : E^1                                                                     |
|                                                                             |
|     +-----------------------------------------------------------------------|
|o7 = |subquotient (| a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab|
|     |                                                                       |
|     |{-4, 4}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 3}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 2}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 1}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 0}                                                                |
|     +-----------------------------------------------------------------------|
|                                                                             |
|o7 : SpectralSequencePage                                                    |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d3 c4 c3d c2d2 cd3 d4 a4bc-a5d a4b3-a6c a5c2-a4b2d a4c3-a4bd2 a3b2c-a4bd a3b4|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-a5bc a4bc2-a3b3d a3bc3-a3b2d2 a3bc2-a4cd a3b3c-a5c2 a4c3-a3b2cd a3c4-a3bcd2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|a3bcd-a4d2 a3b3d-a5cd a4c2d-a3b2d2 a3c3d-a3bd3 a2b3c-a3b2d a2b5-a4b2c a3b2c2-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|a2b4d a2b2c3-a2b3d2 a2b2c2-a3bcd a2b4c-a4bc2 a3bc3-a2b3cd a2bc4-a2b2cd2 a2b2c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d-a3bd2 a2b4d-a4bcd a3bc2d-a2b3d2 a2bc3d-a2b2d3 a2bc3-a3c2d a2b3c2-a4c3 a3c4-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|a2b2c2d a2c5-a2bc2d2 a2bc2d-a3cd2 a2b3cd-a4c2d a3c3d-a2b2cd2 a2c4d-a2bcd3 a2b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|cd2-a3d3 a2b3d2-a4cd2 a3c2d2-a2b2d3 a2c3d2-a2bd4 ab4c-a2b3d ab6-a3b3c a2b3c2-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|ab5d ab3c3-ab4d2 ab3c2-a2b2cd ab5c-a3b2c2 a2b2c3-ab4cd ab2c4-ab3cd2 ab3cd-a2b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2d2 ab5d-a3b2cd a2b2c2d-ab4d2 ab2c3d-ab3d3 ab2c3-a2bc2d ab4c2-a3bc3 a2bc4-ab3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c2d abc5-ab2c2d2 ab2c2d-a2bcd2 ab4cd-a3bc2d a2bc3d-ab3cd2 abc4d-ab2cd3 ab2cd2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-a2bd3 ab4d2-a3bcd2 a2bc2d2-ab3d3 abc3d2-ab2d4 abc4-a2c3d ab3c3-a3c4 a2c5-ab2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c3d ac6-abc3d2 abc3d-a2c2d2 ab3c2d-a3c3d a2c4d-ab2c2d2 ac5d-abc2d3 abc2d2-a2c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d3 ab3cd2-a3c2d2 a2c3d2-ab2cd3 ac4d2-abcd4 abcd3-a2d4 ab3d3-a3cd3 a2c2d3-ab2d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|4 ac3d3-abd5 b5c-ab4d b7-a2b4c ab4c2-b6d b4c3-b5d2 b4c2-ab3cd b6c-a2b3c2 ab3c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|3-b5cd b3c4-b4cd2 b4cd-ab3d2 b6d-a2b3cd ab3c2d-b5d2 b3c3d-b4d3 b3c3-ab2c2d b5|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c2-a2b2c3 ab2c4-b4c2d b2c5-b3c2d2 b3c2d-ab2cd2 b5cd-a2b2c2d ab2c3d-b4cd2 b2c4|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d-b3cd3 b3cd2-ab2d3 b5d2-a2b2cd2 ab2c2d2-b4d3 b2c3d2-b3d4 b2c4-abc3d b4c3-a2b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c4 abc5-b3c3d bc6-b2c3d2 b2c3d-abc2d2 b4c2d-a2bc3d abc4d-b3c2d2 bc5d-b2c2d3 b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2c2d2-abcd3 b4cd2-a2bc2d2 abc3d2-b3cd3 bc4d2-b2cd4 b2cd3-abd4 b4d3-a2bcd3 abc|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2d3-b3d4 bc3d3-b2d5 bc5-ac4d b3c4-a2c5 ac6-b2c4d c7-bc4d2 bc4d-ac3d2 b3c3d-a2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c4d ac5d-b2c3d2 c6d-bc3d3 bc3d2-ac2d3 b3c2d2-a2c3d2 ac4d2-b2c2d3 c5d2-bc2d4 b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c2d3-acd4 b3cd3-a2c2d3 ac3d3-b2cd4 c4d3-bcd5 bcd4-ad5 b3d4-a2cd4 ac2d4-b2d5 c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|3d4-bd6 0 |, | a4bc-a5d a4b3-a6c a5c2-a4b2d a4c3-a4bd2 a3b2c-a4bd a3b4-a5bc a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|4bc2-a3b3d a3bc3-a3b2d2 a3bc2-a4cd a3b3c-a5c2 a4c3-a3b2cd a3c4-a3bcd2 a3bcd-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|4d2 a3b3d-a5cd a4c2d-a3b2d2 a3c3d-a3bd3 a2b3c-a3b2d a2b5-a4b2c a3b2c2-a2b4d a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2b2c3-a2b3d2 a2b2c2-a3bcd a2b4c-a4bc2 a3bc3-a2b3cd a2bc4-a2b2cd2 a2b2cd-a3bd2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| a2b4d-a4bcd a3bc2d-a2b3d2 a2bc3d-a2b2d3 a2bc3-a3c2d a2b3c2-a4c3 a3c4-a2b2c2d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| a2c5-a2bc2d2 a2bc2d-a3cd2 a2b3cd-a4c2d a3c3d-a2b2cd2 a2c4d-a2bcd3 a2bcd2-a3d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|3 a2b3d2-a4cd2 a3c2d2-a2b2d3 a2c3d2-a2bd4 ab4c-a2b3d ab6-a3b3c a2b3c2-ab5d ab|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|3c3-ab4d2 ab3c2-a2b2cd ab5c-a3b2c2 a2b2c3-ab4cd ab2c4-ab3cd2 ab3cd-a2b2d2 ab5|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d-a3b2cd a2b2c2d-ab4d2 ab2c3d-ab3d3 ab2c3-a2bc2d ab4c2-a3bc3 a2bc4-ab3c2d abc|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|5-ab2c2d2 ab2c2d-a2bcd2 ab4cd-a3bc2d a2bc3d-ab3cd2 abc4d-ab2cd3 ab2cd2-a2bd3 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|ab4d2-a3bcd2 a2bc2d2-ab3d3 abc3d2-ab2d4 abc4-a2c3d ab3c3-a3c4 a2c5-ab2c3d ac6|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-abc3d2 abc3d-a2c2d2 ab3c2d-a3c3d a2c4d-ab2c2d2 ac5d-abc2d3 abc2d2-a2cd3 ab3c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d2-a3c2d2 a2c3d2-ab2cd3 ac4d2-abcd4 abcd3-a2d4 ab3d3-a3cd3 a2c2d3-ab2d4 ac3d3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-abd5 b5c-ab4d b7-a2b4c ab4c2-b6d b4c3-b5d2 b4c2-ab3cd b6c-a2b3c2 ab3c3-b5cd |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|b3c4-b4cd2 b4cd-ab3d2 b6d-a2b3cd ab3c2d-b5d2 b3c3d-b4d3 b3c3-ab2c2d b5c2-a2b2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c3 ab2c4-b4c2d b2c5-b3c2d2 b3c2d-ab2cd2 b5cd-a2b2c2d ab2c3d-b4cd2 b2c4d-b3cd3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| b3cd2-ab2d3 b5d2-a2b2cd2 ab2c2d2-b4d3 b2c3d2-b3d4 b2c4-abc3d b4c3-a2bc4 abc5|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-b3c3d bc6-b2c3d2 b2c3d-abc2d2 b4c2d-a2bc3d abc4d-b3c2d2 bc5d-b2c2d3 b2c2d2-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|bcd3 b4cd2-a2bc2d2 abc3d2-b3cd3 bc4d2-b2cd4 b2cd3-abd4 b4d3-a2bcd3 abc2d3-b3d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|4 bc3d3-b2d5 bc5-ac4d b3c4-a2c5 ac6-b2c4d c7-bc4d2 bc4d-ac3d2 b3c3d-a2c4d ac5|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d-b2c3d2 c6d-bc3d3 bc3d2-ac2d3 b3c2d2-a2c3d2 ac4d2-b2c2d3 c5d2-bc2d4 bc2d3-ac|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d4 b3cd3-a2c2d3 ac3d3-b2cd4 c4d3-bcd5 bcd4-ad5 b3d4-a2cd4 ac2d4-b2d5 c3d4-bd6|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----+-----------------------------------------------------------------------|
| 0 |)|subquotient ({2} | a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   |
|     |             {3} | 0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d |
|     |             {3} | 0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   |
|     |             {3} | 0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   |
|     |                                                                       |
|     |{-3, 4}                                                                |
|-----+-----------------------------------------------------------------------|
|     |subquotient (| a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3 b2c b2d bc2 bc|
|     |                                                                       |
|     |{-3, 3}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|-----+-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-3, 2}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|-----+-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-3, 1}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|-----+-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-3, 0}                                                                |
|-----+-----------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0|
|0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   a|
|a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0|
|0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d bd2 c3 c2d cd2 d3 a3bc-a4d a3b3-a5c a4c2-a3b2d a3c3-a3bd2 a2b2c-a3bd a2b4-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0 |
|cd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc|
|   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0 |
|   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|4bc a3bc2-a2b3d a2bc3-a2b2d2 a2bc2-a3cd a2b3c-a4c2 a3c3-a2b2cd a2c4-a2bcd2 a2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  0   0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0  |
|2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2|
|  bc2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0  |
|  0   bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bcd-a3d2 a2b3d-a4cd a3c2d-a2b2d2 a2c3d-a2bd3 ab3c-a2b2d ab5-a3b2c a2b2c2-ab4d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   0   d3 0  0  0  -a3b2 -a4c -a3bd -a3c2 -a2b3 -a3bc -a2b2d -a2bc2 -a2b2c |
| 0   0   0  d3 0  0  a3c   a3d  0     0     a2bc  a2bd  0      0      a2c2   |
| cd2 0   0  0  d3 0  a4    a3b  -a3c  -a3d  a3b   a2b2  -a2bc  -a2bd  a3c    |
| 0   cd2 0  0  0  d3 0     0    a4    a3b   0     0     a3b    a2b2   0      |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| ab2c3-ab3d2 ab2c2-a2bcd ab4c-a3bc2 a2bc3-ab3cd abc4-ab2cd2 ab2cd-a2bd2 ab4d-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-a3c2 -a2bcd -a2c3 -a2b2d -a3cd -a2bd2 -a2c2d -ab4 -a2b2c -ab3d -ab2c2 -ab3c |
|a2cd  0      0     a2cd   a2d2  0      0      ab2c ab2d   0     0      abc2  |
|a2bc  -a2c2  -a2cd a3d    a2bd  -a2cd  -a2d2  a2b2 ab3    -ab2c -ab2d  a2bc  |
|0     a3c    a2bc  0      0     a3d    a2bd   0    0      a2b2  ab3    0     |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a3bcd a2bc2d-ab3d2 abc3d-ab2d3 abc3-a2c2d ab3c2-a3c3 a2c4-ab2c2d ac5-abc2d2 a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-a2bc2 -ab2cd -abc3 -ab3d -a2bcd -ab2d2 -abc2d -ab2c2 -a2c3 -abc2d -ac4  -ab2|
|abcd   0      0     abcd  abd2   0      0      ac3    ac2d  0      0     ac2d|
|ab2c   -abc2  -abcd a2bd  ab2d   -abcd  -abd2  a2c2   abc2  -ac3   -ac2d a2cd|
|0      a2bc   ab2c  0     0      a2bd   ab2d   0      0     a2c2   abc2  0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bc2d-a2cd2 ab3cd-a3c2d a2c3d-ab2cd2 ac4d-abcd3 abcd2-a2d3 ab3d2-a3cd2 a2c2d2-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|cd -a2c2d -abcd2 -ac3d -ab2d2 -a2cd2 -abd3 -ac2d2 -b5 -ab3c -b4d -b3c2 -b4c -|
|   acd2   0      0     acd2   ad3    0     0      b3c b3d   0    0     b2c2 b|
|   abcd   -ac2d  -acd2 a2d2   abd2   -acd2 -ad3   ab3 b4    -b3c -b3d  ab2c b|
|   0      a2cd   abcd  0      0      a2d2  abd2   0   0     ab3  b4    0    0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|ab2d3 ac3d2-abd4 b4c-ab3d b6-a2b3c ab3c2-b5d b3c3-b4d2 b3c2-ab2cd b5c-a2b2c2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|ab2c2 -b3cd -b2c3 -b4d -ab2cd -b3d2 -b2c2d -b3c2 -abc3 -b2c2d -bc4  -b3cd -ab|
|2cd   0     0     b2cd b2d2   0     0      bc3   bc2d  0      0     bc2d  bcd|
|3c    -b2c2 -b2cd ab2d b3d    -b2cd -b2d2  abc2  b2c2  -bc3   -bc2d abcd  b2c|
|      ab2c  b3c   0    0      ab2d  b3d    0     0     abc2   b2c2  0     0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|ab2c3-b4cd b2c4-b3cd2 b3cd-ab2d2 b5d-a2b2cd ab2c2d-b4d2 b2c3d-b3d3 b2c3-abc2d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c2d -b2cd2 -bc3d -b3d2 -abcd2 -b2d3 -bc2d2 -b2c3 -ac4 -bc3d -c5  -b2c2d -ac3d|
|2   0      0     bcd2  bd3    0     0      c4    c3d  0     0    c3d    c2d2 |
|d   -bc2d  -bcd2 abd2  b2d2   -bcd2 -bd3   ac3   bc3  -c4   -c3d ac2d   bc2d |
|    abcd   b2cd  0     0      abd2  b2d2   0     0    ac3   bc3  0      0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| b4c2-a2bc3 abc4-b3c2d bc5-b2c2d2 b2c2d-abcd2 b4cd-a2bc2d abc3d-b3cd2 bc4d-b2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| -bc2d2 -c4d  -b2cd2 -ac2d2 -bcd3 -c3d2 -b2d3 -acd3 -bd4 -c2d3 a4 0  0  0  a3|
| 0      0     c2d2   cd3    0     0     cd3   d4    0    0     0  a4 0  0  0 |
| -c3d   -c2d2 acd2   bcd2   -c2d2 -cd3  ad3   bd3   -cd3 -d4   0  0  a4 0  0 |
| ac2d   bc2d  0      0      acd2  bcd2  0     0     ad3  bd3   0  0  0  a4 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|cd3 b2cd2-abd3 b4d2-a2bcd2 abc2d2-b3d3 bc3d2-b2d4 bc4-ac3d b3c3-a2c4 ac5-b2c3|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|b 0   0   0   a3c 0   0   0   a3d 0   0   0   a2b2 0    0    0    a2bc 0    0|
|  a3b 0   0   0   a3c 0   0   0   a3d 0   0   0    a2b2 0    0    0    a2bc 0|
|  0   a3b 0   0   0   a3c 0   0   0   a3d 0   0    0    a2b2 0    0    0    a|
|  0   0   a3b 0   0   0   a3c 0   0   0   a3d 0    0    0    a2b2 0    0    0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d c6-bc3d2 bc3d-ac2d2 b3c2d-a2c3d ac4d-b2c2d2 c5d-bc2d3 bc2d2-acd3 b3cd2-a2c2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0  |
|    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d|
|2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0  |
|    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2 ac3d2-b2cd3 c4d2-bcd4 bcd3-ad4 b3d3-a2cd3 ac2d3-b2d4 c3d3-bd5 a4 a3b a3c a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  0    0    ab3 0   0   0   ab2c 0    0    0    ab2d 0    0    0    abc2 0   |
|2 0    0    0   ab3 0   0   0    ab2c 0    0    0    ab2d 0    0    0    abc2|
|  a2d2 0    0   0   ab3 0   0    0    ab2c 0    0    0    ab2d 0    0    0   |
|  0    a2d2 0   0   0   ab3 0    0    0    ab2c 0    0    0    ab2d 0    0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab2d abc2 abcd abd2 ac3 ac2d acd2 a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0    0    abcd 0    0    0    abd2 0    0    0    ac3 0   0   0   ac2d 0    |
| 0    0    0    abcd 0    0    0    abd2 0    0    0   ac3 0   0   0    ac2d |
| abc2 0    0    0    abcd 0    0    0    abd2 0    0   0   ac3 0   0    0    |
| 0    abc2 0    0    0    abcd 0    0    0    abd2 0   0   0   ac3 0    0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 bd3 c4 c3d c2d2 cd3 d4 |, | a3bc-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0    0    acd2 0    0    0    ad3 0   0   0   b4 0  0  0  b3c 0   0   0   b3d|
|0    0    0    acd2 0    0    0   ad3 0   0   0  b4 0  0  0   b3c 0   0   0  |
|ac2d 0    0    0    acd2 0    0   0   ad3 0   0  0  b4 0  0   0   b3c 0   0  |
|0    ac2d 0    0    0    acd2 0   0   0   ad3 0  0  0  b4 0   0   0   b3c 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|4d a3b3-a5c a4c2-a3b2d a3c3-a3bd2 a2b2c-a3bd a2b4-a4bc a3bc2-a2b3d a2bc3-a2b2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   0   0   b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0    bc3 |
| b3d 0   0   0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0   |
| 0   b3d 0   0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0   |
| 0   0   b3d 0    0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2 a2bc2-a3cd a2b3c-a4c2 a3c3-a2b2cd a2c4-a2bcd2 a2bcd-a3d2 a2b3d-a4cd a3c2d-|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0   0   0   bc2d 0    0    0    bcd2 0    0    0    bd3 0   0   0   c4 0  0  |
|bc3 0   0   0    bc2d 0    0    0    bcd2 0    0    0   bd3 0   0   0  c4 0  |
|0   bc3 0   0    0    bc2d 0    0    0    bcd2 0    0   0   bd3 0   0  0  c4 |
|0   0   bc3 0    0    0    bc2d 0    0    0    bcd2 0   0   0   bd3 0  0  0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a2b2d2 a2c3d-a2bd3 ab3c-a2b2d ab5-a3b2c a2b2c2-ab4d ab2c3-ab3d2 ab2c2-a2bcd a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0  c3d 0   0   0   c2d2 0    0    0    cd3 0   0   0   d4 0  0  0  |, {2} | -|
|0  0   c3d 0   0   0    c2d2 0    0    0   cd3 0   0   0  d4 0  0  |  {3} | a|
|0  0   0   c3d 0   0    0    c2d2 0    0   0   cd3 0   0  0  d4 0  |  {3} | a|
|c4 0   0   0   c3d 0    0    0    c2d2 0   0   0   cd3 0  0  0  d4 |  {3} | 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b4c-a3bc2 a2bc3-ab3cd abc4-ab2cd2 ab2cd-a2bd2 ab4d-a3bcd a2bc2d-ab3d2 abc3d-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|a3b2 -a4c -a3bd -a3c2 -a2b3 -a3bc -a2b2d -a2bc2 -a2b2c -a3c2 -a2bcd -a2c3 -a2|
|3c   a3d  0     0     a2bc  a2bd  0      0      a2c2   a2cd  0      0     a2c|
|4    a3b  -a3c  -a3d  a3b   a2b2  -a2bc  -a2bd  a3c    a2bc  -a2c2  -a2cd a3d|
|     0    a4    a3b   0     0     a3b    a2b2   0      0     a3c    a2bc  0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b2d3 abc3-a2c2d ab3c2-a3c3 a2c4-ab2c2d ac5-abc2d2 abc2d-a2cd2 ab3cd-a3c2d a2c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|b2d -a3cd -a2bd2 -a2c2d -ab4 -a2b2c -ab3d -ab2c2 -ab3c -a2bc2 -ab2cd -abc3 -a|
|d   a2d2  0      0      ab2c ab2d   0     0      abc2  abcd   0      0     ab|
|    a2bd  -a2cd  -a2d2  a2b2 ab3    -ab2c -ab2d  a2bc  ab2c   -abc2  -abcd a2|
|    0     a3d    a2bd   0    0      a2b2  ab3    0     0      a2bc   ab2c  0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3d-ab2cd2 ac4d-abcd3 abcd2-a2d3 ab3d2-a3cd2 a2c2d2-ab2d3 ac3d2-abd4 b4c-ab3d |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|b3d -a2bcd -ab2d2 -abc2d -ab2c2 -a2c3 -abc2d -ac4  -ab2cd -a2c2d -abcd2 -ac3d|
|cd  abd2   0      0      ac3    ac2d  0      0     ac2d   acd2   0      0    |
|bd  ab2d   -abcd  -abd2  a2c2   abc2  -ac3   -ac2d a2cd   abcd   -ac2d  -acd2|
|    0      a2bd   ab2d   0      0     a2c2   abc2  0      0      a2cd   abcd |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b6-a2b3c ab3c2-b5d b3c3-b4d2 b3c2-ab2cd b5c-a2b2c2 ab2c3-b4cd b2c4-b3cd2 b3cd|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| -ab2d2 -a2cd2 -abd3 -ac2d2 -b5 -ab3c -b4d -b3c2 -b4c -ab2c2 -b3cd -b2c3 -b4d|
| acd2   ad3    0     0      b3c b3d   0    0     b2c2 b2cd   0     0     b2cd|
| a2d2   abd2   -acd2 -ad3   ab3 b4    -b3c -b3d  ab2c b3c    -b2c2 -b2cd ab2d|
| 0      0      a2d2  abd2   0   0     ab3  b4    0    0      ab2c  b3c   0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-ab2d2 b5d-a2b2cd ab2c2d-b4d2 b2c3d-b3d3 b2c3-abc2d b4c2-a2bc3 abc4-b3c2d bc5|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| -ab2cd -b3d2 -b2c2d -b3c2 -abc3 -b2c2d -bc4  -b3cd -abc2d -b2cd2 -bc3d -b3d2|
| b2d2   0     0      bc3   bc2d  0      0     bc2d  bcd2   0      0     bcd2 |
| b3d    -b2cd -b2d2  abc2  b2c2  -bc3   -bc2d abcd  b2cd   -bc2d  -bcd2 abd2 |
| 0      ab2d  b3d    0     0     abc2   b2c2  0     0      abcd   b2cd  0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-b2c2d2 b2c2d-abcd2 b4cd-a2bc2d abc3d-b3cd2 bc4d-b2cd3 b2cd2-abd3 b4d2-a2bcd2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| -abcd2 -b2d3 -bc2d2 -b2c3 -ac4 -bc3d -c5  -b2c2d -ac3d -bc2d2 -c4d  -b2cd2 -|
| bd3    0     0      c4    c3d  0     0    c3d    c2d2  0      0     c2d2   c|
| b2d2   -bcd2 -bd3   ac3   bc3  -c4   -c3d ac2d   bc2d  -c3d   -c2d2 acd2   b|
| 0      abd2  b2d2   0     0    ac3   bc3  0      0     ac2d   bc2d  0      0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| abc2d2-b3d3 bc3d2-b2d4 bc4-ac3d b3c3-a2c4 ac5-b2c3d c6-bc3d2 bc3d-ac2d2 b3c2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|ac2d2 -bcd3 -c3d2 -b2d3 -acd3 -bd4 -c2d3 a4 0  0  0  a3b 0   0   0   a3c 0   |
|d3    0     0     cd3   d4    0    0     0  a4 0  0  0   a3b 0   0   0   a3c |
|cd2   -c2d2 -cd3  ad3   bd3   -cd3 -d4   0  0  a4 0  0   0   a3b 0   0   0   |
|      acd2  bcd2  0     0     ad3  bd3   0  0  0  a4 0   0   0   a3b 0   0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d-a2c3d ac4d-b2c2d2 c5d-bc2d3 bc2d2-acd3 b3cd2-a2c2d2 ac3d2-b2cd3 c4d2-bcd4 b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0   0   a3d 0   0   0   a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0  |
|0   0   0   a3d 0   0   0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0  |
|a3c 0   0   0   a3d 0   0    0    a2b2 0    0    0    a2bc 0    0    0    a2b|
|0   a3c 0   0   0   a3d 0    0    0    a2b2 0    0    0    a2bc 0    0    0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|cd3-ad4 b3d3-a2cd3 ac2d3-b2d4 c3d3-bd5 a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0    0    ab3 0   0 |
|  0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0    0   ab3 0 |
|d 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0   0   ab|
|  a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0   0   0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d a2d2 ab3 ab2c ab2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  0   ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0|
|  0   0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0|
|3 0   0    0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    a|
|  ab3 0    0    0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2 bc3 bc2d bcd2 bd3 c4 c3d c2d2 cd3 d4 |)                                   |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|    0    abd2 0    0    0    ac3 0   0   0   ac2d 0    0    0    acd2 0    0 |
|    0    0    abd2 0    0    0   ac3 0   0   0    ac2d 0    0    0    acd2 0 |
|bcd 0    0    0    abd2 0    0   0   ac3 0   0    0    ac2d 0    0    0    ac|
|    abcd 0    0    0    abd2 0   0   0   ac3 0    0    0    ac2d 0    0    0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|   0    ad3 0   0   0   b4 0  0  0  b3c 0   0   0   b3d 0   0   0   b2c2 0   |
|   0    0   ad3 0   0   0  b4 0  0  0   b3c 0   0   0   b3d 0   0   0    b2c2|
|d2 0    0   0   ad3 0   0  0  b4 0  0   0   b3c 0   0   0   b3d 0   0    0   |
|   acd2 0   0   0   ad3 0  0  0  b4 0   0   0   b3c 0   0   0   b3d 0    0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0    0    b2cd 0    0    0    b2d2 0    0    0    bc3 0   0   0   bc2d 0    |
| 0    0    0    b2cd 0    0    0    b2d2 0    0    0   bc3 0   0   0    bc2d |
| b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0   0   bc3 0   0    0    |
| 0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0   0   0   bc3 0    0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0    0    bcd2 0    0    0    bd3 0   0   0   c4 0  0  0  c3d 0   0   0   c2d|
|0    0    0    bcd2 0    0    0   bd3 0   0   0  c4 0  0  0   c3d 0   0   0  |
|bc2d 0    0    0    bcd2 0    0   0   bd3 0   0  0  c4 0  0   0   c3d 0   0  |
|0    bc2d 0    0    0    bcd2 0   0   0   bd3 0  0  0  c4 0   0   0   c3d 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------+-----------------------------|
|2 0    0    0    cd3 0   0   0   d4 0  0  0  |)|subquotient ({4} | a2 0  0  0|
|  c2d2 0    0    0   cd3 0   0   0  d4 0  0  | |             {4} | 0  a2 0  0|
|  0    c2d2 0    0   0   cd3 0   0  0  d4 0  | |             {4} | 0  0  a2 0|
|  0    0    c2d2 0   0   0   cd3 0  0  0  d4 | |             {4} | 0  0  0  a|
|                                               |                             |
|                                               |{-2, 4}                      |
|-----------------------------------------------+-----------------------------|
|                                               |subquotient ({2} | a2 0  0  0|
|                                               |             {3} | 0  a2 0  0|
|                                               |             {3} | 0  0  a2 0|
|                                               |             {3} | 0  0  0  a|
|                                               |                             |
|                                               |{-2, 3}                      |
|-----------------------------------------------+-----------------------------|
|                                               |subquotient (| a2 ab ac ad b2|
|                                               |                             |
|                                               |{-2, 2}                      |
|                                               |                             |
|                                               |                             |
|                                               |                             |
|-----------------------------------------------+-----------------------------|
|                                               |0                            |
|                                               |                             |
|                                               |{-2, 1}                      |
|                                               |                             |
|                                               |                             |
|                                               |                             |
|-----------------------------------------------+-----------------------------|
|                                               |0                            |
|                                               |                             |
|                                               |{-2, 0}                      |
|-----------------------------------------------+-----------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 |
|  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  |
|  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  |
|2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 |
|  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  |
|  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  |
|2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| bc bd c2 cd d2 a2bc-a3d a2b3-a4c a3c2-a2b2d a2c3-a2bd2 ab2c-a2bd ab4-a3bc a2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0  0  0  cd 0  0  0  d2 0  0  0  a2d  abd  acd  ad2  b2d  bcd  bd2  c2d  cd2 |
|c2 0  0  0  cd 0  0  0  d2 0  0  -a2c -abc -ac2 -acd -b2c -bc2 -bcd -c3  -c2d|
|0  c2 0  0  0  cd 0  0  0  d2 0  -a2b -ab2 -abc -abd -b3  -b2c -b2d -bc2 -bcd|
|0  0  c2 0  0  0  cd 0  0  0  d2 a3   a2b  a2c  a2d  ab2  abc  abd  ac2  acd |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|0  0  0  cd 0  0  0  d2 0  0  0  -a2b2 -a3c -a2bd -a2c2 -ab3 -a2bc -ab2d -abc|
|c2 0  0  0  cd 0  0  0  d2 0  0  a2c   a2d  0     0     abc  abd   0     0   |
|0  c2 0  0  0  cd 0  0  0  d2 0  a3    a2b  -a2c  -a2d  a2b  ab2   -abc  -abd|
|0  0  c2 0  0  0  cd 0  0  0  d2 0     0    a3    a2b   0    0     a2b   ab2 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bc2-ab3d abc3-ab2d2 abc2-a2cd ab3c-a3c2 a2c3-ab2cd ac4-abcd2 abcd-a2d2 ab3d-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| d3   a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0  |
| -cd2 0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0  |
| -bd2 0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2|
| ad2  0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2 -ab2c -a2c2 -abcd -ac3 -ab2d -a2cd -abd2 -ac2d -b4 -ab2c -b3d -b2c2 -b3c -a|
|  ac2   acd   0     0    acd   ad2   0     0     b2c b2d   0    0     bc2  bc|
|  a2c   abc   -ac2  -acd a2d   abd   -acd  -ad2  ab2 b3    -b2c -b2d  abc  b2|
|  0     0     a2c   abc  0     0     a2d   abd   0   0     ab2  b3    0    0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3cd a2c2d-ab2d2 ac3d-abd3 b3c-ab2d b5-a2b2c ab2c2-b4d b2c3-b3d2 b2c2-abcd b4c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   |
| 0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 |
| 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   |
| ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bc2 -b2cd -bc3 -b3d -abcd -b2d2 -bc2d -b2c2 -ac3 -bc2d -c4  -b2cd -ac2d -bcd2|
|d   0     0    bcd  bd2   0     0     c3    c2d  0     0    c2d   cd2   0    |
|c   -bc2  -bcd abd  b2d   -bcd  -bd2  ac2   bc2  -c3   -c2d acd   bcd   -c2d |
|    abc   b2c  0    0     abd   b2d   0     0    ac2   bc2  0     0     acd  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-a2bc2 abc3-b3cd bc4-b2cd2 b2cd-abd2 b4d-a2bcd abc2d-b3d2 bc3d-b2d3 bc3-ac2d |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0|
|0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0|
|ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   b|
|0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| -c3d -b2d2 -acd2 -bd3 -c2d2 a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d |
| 0    cd2   d3    0    0     0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   |
| -cd2 ad2   bd2   -cd2 -d3   0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   |
| bcd  0     0     ad2  bd2   0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b3c2-a2c3 ac4-b2c2d c5-bc2d2 bc2d-acd2 b3cd-a2c2d ac3d-b2cd2 c4d-bcd3 bcd2-ad|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0   0   d3 0  0  0|
|   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0   0   0  d3 0  0|
|cd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2 0   0  0  d3 0|
|   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0   cd2 0  0  0  d|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   a|
|a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0|
|0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0|
|0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|3 b3d2-a2cd2 ac2d2-b2d3 c3d2-bd4 a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3 b2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  |, {4} | a2d  abd  acd  ad2  b2d  bcd  bd2  c2d  cd2  d3   a3 0  0  0  a2b |
|  |  {4} | -a2c -abc -ac2 -acd -b2c -bc2 -bcd -c3  -c2d -cd2 0  a3 0  0  0   |
|  |  {4} | -a2b -ab2 -abc -abd -b3  -b2c -b2d -bc2 -bcd -bd2 0  0  a3 0  0   |
|3 |  {4} | a3   a2b  a2c  a2d  ab2  abc  abd  ac2  acd  ad2  0  0  0  a3 0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|cd 0   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc|
|   acd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0 |
|   0   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0 |
|   0   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c b2d bc2 bcd bd2 c3 c2d cd2 d3 |, | a2bc-a3d a2b3-a4c a3c2-a2b2d a2c3-a2bd2 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   a|
|a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0|
|0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0|
|0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2 0   0   0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2|
|  bc2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0  |
|  0   bc2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0  |
|  0   0   bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|ab2c-a2bd ab4-a3bc a2bc2-ab3d abc3-ab2d2 abc2-a2cd ab3c-a3c2 a2c3-ab2cd ac4-a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|bd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0   b3 0  0  0  b2|
|   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0  b3 0  0  0 |
|   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0  0  b3 0  0 |
|   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0  0  0  b3 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0   0   0   d3 0  0  0  |, {2} | -a2b2 -a3c -a2bd -a2c2 -ab3 -a2bc -ab2d -ab|
| cd2 0   0   0  d3 0  0  |  {3} | a2c   a2d  0     0     abc  abd   0     0  |
| 0   cd2 0   0  0  d3 0  |  {3} | a3    a2b  -a2c  -a2d  a2b  ab2   -abc  -ab|
| 0   0   cd2 0  0  0  d3 |  {3} | 0     0    a3    a2b   0    0     a2b   ab2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bcd2 abcd-a2d2 ab3d-a3cd a2c2d-ab2d2 ac3d-abd3 b3c-ab2d b5-a2b2c ab2c2-b4d b2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0  |
|  b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0  |
|  0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0  |
|  0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2 -ab2c -a2c2 -abcd -ac3 -ab2d -a2cd -abd2 -ac2d -b4 -ab2c -b3d -b2c2 -b3c -|
|   ac2   acd   0     0    acd   ad2   0     0     b2c b2d   0    0     bc2  b|
|d  a2c   abc   -ac2  -acd a2d   abd   -acd  -ad2  ab2 b3    -b2c -b2d  abc  b|
|   0     0     a2c   abc  0     0     a2d   abd   0   0     ab2  b3    0    0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c3-b3d2 b2c2-abcd b4c-a2bc2 abc3-b3cd bc4-b2cd2 b2cd-abd2 b4d-a2bcd abc2d-b3d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| c3 0  0  0  c2d 0   0   0   cd2 0   0   0   d3 0  0  0  |)                  |
| 0  c3 0  0  0   c2d 0   0   0   cd2 0   0   0  d3 0  0  |                   |
| 0  0  c3 0  0   0   c2d 0   0   0   cd2 0   0  0  d3 0  |                   |
| 0  0  0  c3 0   0   0   c2d 0   0   0   cd2 0  0  0  d3 |                   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|abc2 -b2cd -bc3 -b3d -abcd -b2d2 -bc2d -b2c2 -ac3 -bc2d -c4  -b2cd -ac2d -bcd|
|cd   0     0    bcd  bd2   0     0     c3    c2d  0     0    c2d   cd2   0   |
|2c   -bc2  -bcd abd  b2d   -bcd  -bd2  ac2   bc2  -c3   -c2d acd   bcd   -c2d|
|     abc   b2c  0    0     abd   b2d   0     0    ac2   bc2  0     0     acd |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2 bc3d-b2d3 bc3-ac2d b3c2-a2c3 ac4-b2c2d c5-bc2d2 bc2d-acd2 b3cd-a2c2d ac3d-b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2 -c3d -b2d2 -acd2 -bd3 -c2d2 a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d|
|  0    cd2   d3    0    0     0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0  |
|  -cd2 ad2   bd2   -cd2 -d3   0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0  |
|  bcd  0     0     ad2  bd2   0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2cd2 c4d-bcd3 bcd2-ad3 b3d2-a2cd2 ac2d2-b2d3 c3d2-bd4 a3 a2b a2c a2d ab2 abc |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   |
| a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   |
| 0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   |
| 0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|abd ac2 acd ad2 b3 b2c b2d bc2 bcd bd2 c3 c2d cd2 d3 |)                      |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|acd 0   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   b|
|0   acd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0|
|0   0   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0|
|0   0   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2 0   0   0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd|
|   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0 |
|   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0 |
|   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|----------------------------+------------------------------------------------|
|                            |subquotient ({5} | a b c d a2 ab ac ad b2 bc bd |
|                            |                                                |
|                            |{-1, 4}                                         |
|                            |                                                |
|                            |                                                |
|                            |                                                |
|----------------------------+------------------------------------------------|
|2 0   0   0   d3 0  0  0  |)|subquotient ({4} | a 0 0 0 b 0 0 0 c 0 0 0 d 0 0|
|  cd2 0   0   0  d3 0  0  | |             {4} | 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0|
|  0   cd2 0   0  0  d3 0  | |             {4} | 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d|
|  0   0   cd2 0  0  0  d3 | |             {4} | 0 0 0 a 0 0 0 b 0 0 0 c 0 0 0|
|                            |                                                |
|                            |{-1, 3}                                         |
|----------------------------+------------------------------------------------|
|                            |subquotient ({2} | a 0 0 0 b 0 0 0 c 0 0 0 d 0 0|
|                            |             {3} | 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0|
|                            |             {3} | 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d|
|                            |             {3} | 0 0 0 a 0 0 0 b 0 0 0 c 0 0 0|
|                            |                                                |
|                            |{-1, 2}                                         |
|----------------------------+------------------------------------------------|
|                            |subquotient (| a b c d abc-a2d ab3-a3c a2c2-ab2d|
|                            |                                                |
|                            |{-1, 1}                                         |
|                            |                                                |
|                            |                                                |
|                            |                                                |
|----------------------------+------------------------------------------------|
|                            |0                                               |
|                            |                                                |
|                            |{-1, 0}                                         |
|----------------------------+------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|c2 cd d2 |, {5} | a2 ab ac ad b2 bc bd c2 cd d2 |)                           |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0 ad  bd  cd  d2  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0|
| 0 -ac -bc -c2 -cd 0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0|
| 0 -ab -b2 -bc -bd 0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0|
| d a2  ab  ac  ad  0  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0 -ab2 -a2c -abd -ac2 -b3 -abc -b2d -bc2 -b2c -ac2 -bcd -c3 -b2d -acd -bd2 -|
| 0 ac   ad   0    0    bc  bd   0    0    c2   cd   0    0   cd   d2   0    0|
| 0 a2   ab   -ac  -ad  ab  b2   -bc  -bd  ac   bc   -c2  -cd ad   bd   -cd  -|
| d 0    0    a2   ab   0   0    ab   b2   0    0    ac   bc  0    0    ad   b|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| ac3-abd2 b2c-abd b4-a2bc abc2-b3d bc3-b2d2 bc2-acd b3c-a2c2 ac3-b2cd c4-bcd2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |, {4} | ad  bd|
|  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |  {4} | -ac -b|
|  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |  {4} | -ab -b|
|2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |  {4} | a2  ab|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2d a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  b|
|    0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0|
|d2  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0|
|d   0  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| bcd-ad2 b3d-a2cd ac2d-b2d2 c3d-bd3 a2 ab ac ad b2 bc bd c2 cd d2 |, | abc-a2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  cd  d2  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0|
|c -c2 -cd 0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0|
|2 -bc -bd 0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  b|
|  ac  ad  0  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |, {2} | -ab2 -a2c -abd -ac2 -|
|  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |  {3} | ac   ad   0    0    b|
|  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |  {3} | a2   ab   -ac  -ad  a|
|  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |  {3} | 0    0    a2   ab   0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d ab3-a3c a2c2-ab2d ac3-abd2 b2c-abd b4-a2bc abc2-b3d bc3-b2d2 bc2-acd b3c-a2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |)                      |
|  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |                       |
|c 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |                       |
|  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |                       |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b3 -abc -b2d -bc2 -b2c -ac2 -bcd -c3 -b2d -acd -bd2 -c2d a2 0  0  0  ab 0  0 |
|c  bd   0    0    c2   cd   0    0   cd   d2   0    0    0  a2 0  0  0  ab 0 |
|b  b2   -bc  -bd  ac   bc   -c2  -cd ad   bd   -cd  -d2  0  0  a2 0  0  0  ab|
|   0    ab   b2   0    0    ac   bc  0    0    ad   bd   0  0  0  a2 0  0  0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|c2 ac3-b2cd c4-bcd2 bcd-ad2 b3d-a2cd ac2d-b2d2 c3d-bd3 a2 ab ac ad b2 bc bd c|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  c|
| 0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0|
| 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0|
| ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2 cd d2 |)                                                                   |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-------------------------+---------------------------------------------------|
|                         |0                                                  |
|                         |                                                   |
|                         |{0, 4}                                             |
|                         |                                                   |
|                         |                                                   |
|                         |                                                   |
|-------------------------+---------------------------------------------------|
|                         |cokernel {5} | a b c d |                           |
|                         |                                                   |
|                         |{0, 3}                                             |
|                         |                                                   |
|                         |                                                   |
|                         |                                                   |
|-------------------------+---------------------------------------------------|
|d 0  0  0  d2 0  0  0  |)|cokernel {4} | d  a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 ||
|  cd 0  0  0  d2 0  0  | |         {4} | -c 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 ||
|  0  cd 0  0  0  d2 0  | |         {4} | -b 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 ||
|  0  0  cd 0  0  0  d2 | |         {4} | a  0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d ||
|                         |                                                   |
|                         |{0, 2}                                             |
|-------------------------+---------------------------------------------------|
|                         |cokernel {2} | -b2 -ac -bd -c2 a 0 0 0 b 0 0 0 c 0 |
|                         |         {3} | c   d   0   0   0 a 0 0 0 b 0 0 0 c |
|                         |         {3} | a   b   -c  -d  0 0 a 0 0 0 b 0 0 0 |
|                         |         {3} | 0   0   a   b   0 0 0 a 0 0 0 b 0 0 |
|                         |                                                   |
|                         |{0, 1}                                             |
|-------------------------+---------------------------------------------------|
|                         |cokernel | bc-ad b3-a2c ac2-b2d c3-bd2 a b c d |   |
|                         |                                                   |
|                         |{0, 0}                                             |
|-------------------------+---------------------------------------------------|
|-----------------------------------------------------------------------------|
|-------------+                                                               |
|             |                                                               |
|             |                                                               |
|             |                                                               |
|             |                                                               |
|             |                                                               |
|             |                                                               |
|-------------+                                                               |
|             |                                                               |
|             |                                                               |
|             |                                                               |
|             |                                                               |
|             |                                                               |
|             |                                                               |
|-------------+                                                               |
|             |                                                               |
|             |                                                               |
|             |                                                               |
|             |                                                               |
|             |                                                               |
|             |                                                               |
|-------------+                                                               |
|0 0 d 0 0 0 ||                                                               |
|0 0 0 d 0 0 ||                                                               |
|c 0 0 0 d 0 ||                                                               |
|0 c 0 0 0 d ||                                                               |
|             |                                                               |
|             |                                                               |
|-------------+                                                               |
|             |                                                               |
|             |                                                               |
|             |                                                               |
|-------------+                                                               |
+-----------------------------------------------------------------------------+
|i8 : E^infinity                                                              |
|                                                                             |
|     +-----------------------------------------------------------------------|
|o8 = |subquotient (| a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab|
|     |                                                                       |
|     |{-4, 4}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 3}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 2}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 1}                                                                |
|     |                                                                       |
|     |                                                                       |
|     |                                                                       |
|     +-----------------------------------------------------------------------|
|     |0                                                                      |
|     |                                                                       |
|     |{-4, 0}                                                                |
|     +-----------------------------------------------------------------------|
|                                                                             |
|o8 : Page                                                                    |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d3 c4 c3d c2d2 cd3 d4 bc-ad b3-a2c ac2-b2d c3-bd2 0 |, | bc-ad b3-a2c ac2-b2d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|------------+----------------------------------------------------------------|
| c3-bd2 0 |)|subquotient ({2} | 0 a2b2 a2bd a2bd 0 a3c  a3c  a2c2 a2b2 ab3  a|
|            |             {3} | 0 -a2c 0    0    0 -a2d -a2d 0    -a2c -abc 0|
|            |             {3} | 0 -a3  a2c  a2c  0 -a2b -a2b a2d  -a3  -a2b a|
|            |             {3} | 0 0    -a3  -a3  0 0    0    -a2b 0    0    -|
|            |                                                                |
|            |{-3, 4}                                                         |
|------------+----------------------------------------------------------------|
|            |subquotient (| a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3 b2c b2d|
|            |                                                                |
|            |{-3, 3}                                                         |
|            |                                                                |
|            |                                                                |
|            |                                                                |
|------------+----------------------------------------------------------------|
|            |0                                                               |
|            |                                                                |
|            |{-3, 2}                                                         |
|            |                                                                |
|            |                                                                |
|            |                                                                |
|------------+----------------------------------------------------------------|
|            |0                                                               |
|            |                                                                |
|            |{-3, 1}                                                         |
|            |                                                                |
|            |                                                                |
|            |                                                                |
|------------+----------------------------------------------------------------|
|            |0                                                               |
|            |                                                                |
|            |{-3, 0}                                                         |
|------------+----------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|b2d ab2d a2bd a2bc a2bc a2bc abc2 abc2 a2c2 ab2c ab2c abcd abcd abcd 0       |
|    0    0    -abd -abd -abd 0    0    0    -ac2 -ac2 0    0    0    acd     |
|bc  abc  a2c  -ab2 -ab2 -ab2 abd  abd  a2d  -a2c -a2c ac2  ac2  ac2  abc+a2d |
|a2b -a2b -a3  0    0    0    -ab2 -ab2 -a2b 0    0    -a2c -a2c -a2c -a2b    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| bc2 bcd bd2 c3 c2d cd2 d3 bc-ad b3-a2c ac2-b2d c3-bd2 a4 a3b a3c a3d a2b2 a2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|abd2 ac3  abd2 0 a2cd a2cd a2cd ac2d ac2d ab3  ab2c b4   b3d  b3d  ab2d 0    |
|0    0    0    0 -ad2 -ad2 -ad2 0    0    -abc -ac2 -b2c 0    0    0    -ac2+|
|acd  acd  acd  0 -abd -abd -abd ad2  ad2  -a2b -a2c -ab2 b2c  b2c  abc  b3-a2|
|-a2d -abc -a2d 0 0    0    0    -abd -abd 0    0    0    -ab2 -ab2 -a2b 0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|    b2c2 b2c2 abc2 b3c  b3c  b2cd b2cd b2cd abcd 0       b2d2 bc3  b2d2 abd2 |
|b2d 0    0    0    -bc2 -bc2 0    0    0    0    bcd     0    0    0    0    |
|c   b2d  b2d  abd  -abc -abc bc2  bc2  bc2  ac2  b2c+abd bcd  bcd  bcd  acd  |
|    -b3  -b3  -ab2 0    0    -abc -abc -abc -a2c -ab2    -abd -b2c -abd -a2d |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 bd3 c4 c3d c2d2 cd3 d4 |, | bc-ad b3-a2c ac2|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0       bc2d bc2d bc3  ac3  0       0        bc2d ac2d 0       bcd2 bcd2 c4  |
|bd2     0    0    0    0    c3      0        0    0    c2d     0    0    0   |
|ac2+b2d bd2  bd2  bcd  acd  ac2+b2d c3-bd2   bd2  ad2  bc2+acd c2d  c2d  c2d |
|-a2c    -b2d -b2d -b2c -abc -b3     -ac2+b2d -b2d -abd -abc    -acd -acd -bc2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-b2d c3-bd2 a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab2d abc2 a|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| bcd2 0       bd3  c3d  c3d  0 bd3  0 acd2 acd2 acd2 c2d2 c2d2 0 0 0         |
| 0    cd2     0    0    0    0 0    0 -d3  -d3  -d3  0    0    0 0 -a2cd     |
| c2d  bcd+ad2 cd2  cd2  cd2  0 cd2  0 -bd2 -bd2 -bd2 d3   d3   0 0 -a2bc-a3d |
| -acd -abd    -ad2 -bcd -bcd 0 -ad2 0 0    0    0    -bd2 -bd2 0 0 a3b       |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 bd3 c4 c3d|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0         0 0 0 0 0 0 0 0 0 0 0 0 0 0          0 0          0          0 0 0 |
|-a2cd     0 0 0 0 0 0 0 0 0 0 0 0 0 -a2c2+ab2d 0 -abcd      -abcd      0 0 0 |
|-a2bc-a3d 0 0 0 0 0 0 0 0 0 0 0 0 0 ab3-a3c    0 -ab2c-a2bd -ab2c-a2bd 0 0 0 |
|a3b       0 0 0 0 0 0 0 0 0 0 0 0 0 0          0 a2b2       a2b2       0 0 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| c2d2 cd3 d4 |)                                                              |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0 0 0 0         0 0 0 0 0 0 0 0 0 0         0          0         0           |
|0 0 0 -ac3+abd2 0 0 0 0 0 0 0 0 0 -abc2+b3d -a2c2+ab2d -ac3+abd2 -ac3+b2cd+ab|
|0 0 0 0         0 0 0 0 0 0 0 0 0 b4-a2bc   ab3-a3c    0         b3c+ab2d    |
|0 0 0 ab3-a3c   0 0 0 0 0 0 0 0 0 0         0          ab3-a3c   -a3c        |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|   0 0 0 0 0 0         0 0 0 0 0 0 0 0 0 0 0 0 0 0 -b2 -ac -bd -c2 a4 0  0  0|
|d2 0 0 0 0 0 -bc3+ac2d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c   d   0   0   0  a4 0  0|
|   0 0 0 0 0 -b3d+a2cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a   b   -c  -d  0  0  a4 0|
|   0 0 0 0 0 b4-a2bc   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0   0   a   b   0  0  0  a|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  a3b 0   0   0   a3c 0   0   0   a3d 0   0   0   a2b2 0    0    0    a2bc 0 |
|  0   a3b 0   0   0   a3c 0   0   0   a3d 0   0   0    a2b2 0    0    0    a2|
|  0   0   a3b 0   0   0   a3c 0   0   0   a3d 0   0    0    a2b2 0    0    0 |
|4 0   0   0   a3b 0   0   0   a3c 0   0   0   a3d 0    0    0    a2b2 0    0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|   0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2|
|bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0   |
|   a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0   |
|   0    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0    0    0    ab3 0   0   0   ab2c 0    0    0    ab2d 0    0    0    abc2 |
| a2d2 0    0    0   ab3 0   0   0    ab2c 0    0    0    ab2d 0    0    0    |
| 0    a2d2 0    0   0   ab3 0   0    0    ab2c 0    0    0    ab2d 0    0    |
| 0    0    a2d2 0   0   0   ab3 0    0    0    ab2c 0    0    0    ab2d 0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0    0    0    abcd 0    0    0    abd2 0    0    0    ac3 0   0   0   ac2d 0|
|abc2 0    0    0    abcd 0    0    0    abd2 0    0    0   ac3 0   0   0    a|
|0    abc2 0    0    0    abcd 0    0    0    abd2 0    0   0   ac3 0   0    0|
|0    0    abc2 0    0    0    abcd 0    0    0    abd2 0   0   0   ac3 0    0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|    0    0    acd2 0    0    0    ad3 0   0   0   b4 0  0  0  b3c 0   0   0  |
|c2d 0    0    0    acd2 0    0    0   ad3 0   0   0  b4 0  0  0   b3c 0   0  |
|    ac2d 0    0    0    acd2 0    0   0   ad3 0   0  0  b4 0  0   0   b3c 0  |
|    0    ac2d 0    0    0    acd2 0   0   0   ad3 0  0  0  b4 0   0   0   b3c|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| b3d 0   0   0   b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0    |
| 0   b3d 0   0   0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    |
| 0   0   b3d 0   0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    |
| 0   0   0   b3d 0    0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|bc3 0   0   0   bc2d 0    0    0    bcd2 0    0    0    bd3 0   0   0   c4 0 |
|0   bc3 0   0   0    bc2d 0    0    0    bcd2 0    0    0   bd3 0   0   0  c4|
|0   0   bc3 0   0    0    bc2d 0    0    0    bcd2 0    0   0   bd3 0   0  0 |
|0   0   0   bc3 0    0    0    bc2d 0    0    0    bcd2 0   0   0   bd3 0  0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0  0  c3d 0   0   0   c2d2 0    0    0    cd3 0   0   0   d4 0  0  0  |, {2}|
| 0  0  0   c3d 0   0   0    c2d2 0    0    0   cd3 0   0   0  d4 0  0  |  {3}|
| c4 0  0   0   c3d 0   0    0    c2d2 0    0   0   cd3 0   0  0  d4 0  |  {3}|
| 0  c4 0   0   0   c3d 0    0    0    c2d2 0   0   0   cd3 0  0  0  d4 |  {3}|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| | -b2 -ac -bd -c2 a4 0  0  0  a3b 0   0   0   a3c 0   0   0   a3d 0   0   0 |
| | c   d   0   0   0  a4 0  0  0   a3b 0   0   0   a3c 0   0   0   a3d 0   0 |
| | a   b   -c  -d  0  0  a4 0  0   0   a3b 0   0   0   a3c 0   0   0   a3d 0 |
| | 0   0   a   b   0  0  0  a4 0   0   0   a3b 0   0   0   a3c 0   0   0   a3|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    |
|  0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    |
|  0    0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    a2c2 |
|d 0    0    0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0    a2cd 0    0    0    a2d2 0    0    0    ab3 0   0   0   ab2c 0    0    0|
|0    0    a2cd 0    0    0    a2d2 0    0    0   ab3 0   0   0    ab2c 0    0|
|0    0    0    a2cd 0    0    0    a2d2 0    0   0   ab3 0   0    0    ab2c 0|
|a2c2 0    0    0    a2cd 0    0    0    a2d2 0   0   0   ab3 0    0    0    a|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0    abd2 0    0  |
|    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0    abd2 0  |
|    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0    abd|
|b2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  0    ac3 0   0   0   ac2d 0    0    0    acd2 0    0    0    ad3 0   0   0 |
|  0    0   ac3 0   0   0    ac2d 0    0    0    acd2 0    0    0   ad3 0   0 |
|2 0    0   0   ac3 0   0    0    ac2d 0    0    0    acd2 0    0   0   ad3 0 |
|  abd2 0   0   0   ac3 0    0    0    ac2d 0    0    0    acd2 0   0   0   ad|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  b4 0  0  0  b3c 0   0   0   b3d 0   0   0   b2c2 0    0    0    b2cd 0    0|
|  0  b4 0  0  0   b3c 0   0   0   b3d 0   0   0    b2c2 0    0    0    b2cd 0|
|  0  0  b4 0  0   0   b3c 0   0   0   b3d 0   0    0    b2c2 0    0    0    b|
|3 0  0  0  b4 0   0   0   b3c 0   0   0   b3d 0    0    0    b2c2 0    0    0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|    0    b2d2 0    0    0    bc3 0   0   0   bc2d 0    0    0    bcd2 0    0 |
|    0    0    b2d2 0    0    0   bc3 0   0   0    bc2d 0    0    0    bcd2 0 |
|2cd 0    0    0    b2d2 0    0   0   bc3 0   0    0    bc2d 0    0    0    bc|
|    b2cd 0    0    0    b2d2 0   0   0   bc3 0    0    0    bc2d 0    0    0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|   0    bd3 0   0   0   c4 0  0  0  c3d 0   0   0   c2d2 0    0    0    cd3 0|
|   0    0   bd3 0   0   0  c4 0  0  0   c3d 0   0   0    c2d2 0    0    0   c|
|d2 0    0   0   bd3 0   0  0  c4 0  0   0   c3d 0   0    0    c2d2 0    0   0|
|   bcd2 0   0   0   bd3 0  0  0  c4 0   0   0   c3d 0    0    0    c2d2 0   0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-------------------------+---------------------------------------------------|
|   0   0   d4 0  0  0  |)|subquotient ({4} | ad  bd  cd  d2  a2d  0 0 -abd 0 |
|d3 0   0   0  d4 0  0  | |             {4} | -ac -bc -c2 -cd -a2c 0 0 abc  0 |
|   cd3 0   0  0  d4 0  | |             {4} | -ab -b2 -bc -bd -a2b 0 0 ab2  0 |
|   0   cd3 0  0  0  d4 | |             {4} | a2  ab  ac  ad  a3   0 0 -a2b 0 |
|                         |                                                   |
|                         |{-2, 4}                                            |
|-------------------------+---------------------------------------------------|
|                         |subquotient ({2} | 0 ab2 abd abd 0 a2c a2c ac2 ab2 |
|                         |             {3} | 0 -ac 0   0   0 -ad -ad 0   -ac |
|                         |             {3} | 0 -a2 ac  ac  0 -ab -ab ad  -a2 |
|                         |             {3} | 0 0   -a2 -a2 0 0   0   -ab 0   |
|                         |                                                   |
|                         |{-2, 3}                                            |
|-------------------------+---------------------------------------------------|
|                         |subquotient (| a2 ab ac ad b2 bc bd c2 cd d2 bc-ad |
|                         |                                                   |
|                         |{-2, 2}                                            |
|                         |                                                   |
|                         |                                                   |
|                         |                                                   |
|-------------------------+---------------------------------------------------|
|                         |0                                                  |
|                         |                                                   |
|                         |{-2, 1}                                            |
|                         |                                                   |
|                         |                                                   |
|                         |                                                   |
|-------------------------+---------------------------------------------------|
|                         |0                                                  |
|                         |                                                   |
|                         |{-2, 0}                                            |
|-------------------------+---------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|0 0 0 -acd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -b2d -abd 0 0 0 -bcd 0 0 0 0 0 0|
|0 0 0 ac2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b2c  abc  0 0 0 bc2  0 0 0 0 0 0|
|0 0 0 abc  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b3   ab2  0 0 0 b2c  0 0 0 0 0 0|
|0 0 0 -a2c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -ab2 -a2b 0 0 0 -abc 0 0 0 0 0 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b3  b2d b2d abd abc abc abc bc2 bc2 ac2 b2c b2c bcd bcd bcd 0     bd2 c3  0 b|
|-bc 0   0   0   -bd -bd -bd 0   0   0   -c2 -c2 0   0   0   cd    0   0   0 0|
|-ab bc  bc  ac  -b2 -b2 -b2 bd  bd  ad  -ac -ac c2  c2  c2  bc+ad cd  cd  0 c|
|0   -ab -ab -a2 0   0   0   -b2 -b2 -ab 0   0   -ac -ac -ac -ab   -ad -bc 0 -|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|b3-a2c ac2-b2d c3-bd2 a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3 b2c b2d bc2 b|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0 0 0 0 0 0 0 0 0 0 0 -c2d -bcd -acd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
| 0 0 0 0 0 0 0 0 0 0 0 c3   bc2  ac2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
| 0 0 0 0 0 0 0 0 0 0 0 bc2  b2c  abc  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
| 0 0 0 0 0 0 0 0 0 0 0 -ac2 -abc -a2c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|d2 0 acd acd acd c2d c2d 0 0 0        0        0 0 0 0 0 0 0 0 0 0 0 0 0 0   |
|   0 -d2 -d2 -d2 0   0   0 0 -acd     -acd     0 0 0 0 0 0 0 0 0 0 0 0 0 -ac2|
|d  0 -bd -bd -bd d2  d2  0 0 -abc-a2d -abc-a2d 0 0 0 0 0 0 0 0 0 0 0 0 0 b3-a|
|ad 0 0   0   0   -bd -bd 0 0 a2b      a2b      0 0 0 0 0 0 0 0 0 0 0 0 0 0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|cd bd2 c3 c2d cd2 d3 |, | bc-ad b3-a2c ac2-b2d c3-bd2 a3 a2b a2c a2d ab2 abc |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0 0 d  a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0|
| 0 0 -c 0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0|
| 0 0 -b 0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   a|
| 0 0 a  0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|     0 0        0        0 0 0 0 0 0 0       0 0 0 0 0 0 0 0 -b2 -ac -bd -c2 |
|+b2d 0 -bcd     -bcd     0 0 0 0 0 0 -c3+bd2 0 0 0 0 0 0 0 0 c   d   0   0   |
|2c   0 -b2c-abd -b2c-abd 0 0 0 0 0 0 0       0 0 0 0 0 0 0 0 a   b   -c  -d  |
|     0 ab2      ab2      0 0 0 0 0 0 b3-a2c  0 0 0 0 0 0 0 0 0   0   a   b   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|abd ac2 acd ad2 b3 b2c b2d bc2 bcd bd2 c3 c2d cd2 d3 |)                      |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0 |
|   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad|
|b2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0 |
|   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   a|
|0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0|
|0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0|
|0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0  |
|2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd|
|  ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0  |
|  0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|bc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0 |
|   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0 |
|   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0 |
|   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0   0   d3 0  0 |
| 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0   0   0  d3 0 |
| bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2 0   0  0  d3|
| 0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0   cd2 0  0  0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0  |
|  0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0  |
|  0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0  |
|2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| 0  |, {4} | d  a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   a|
| 0  |  {4} | -c 0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0|
| 0  |  {4} | -b 0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0|
| d3 |  {4} | a  0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   a2d 0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0   0   d3 0  0  0  |, {|
| 0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0   0   0  d3 0  0  |  {|
| 0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2 0   0  0  d3 0  |  {|
| 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0   cd2 0  0  0  d3 |  {|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|b2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0 |
|   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0 |
|   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0 |
|   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   ac|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|2} | -b2 -ac -bd -c2 a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   |
|3} | c   d   0   0   0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   |
|3} | a   b   -c  -d  0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d |
|3} | 0   0   a   b   0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|  ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0   0  |
|  0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0   0  |
|  0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc2 0  |
|d 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0   bc2|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0|
|0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0|
|0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   a|
|a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0   0   |
| 0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0   0   |
| 0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2 0   |
| 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0   cd2 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0 |
|   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0 |
|cd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc|
|   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|d3 0  0  0  |)                                                               |
|0  d3 0  0  |                                                                |
|0  0  d3 0  |                                                                |
|0  0  0  d3 |                                                                |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0  |
|  0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0  |
|2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2|
|  bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-------------------+---------------------------------------------------------|
|                   |subquotient ({5} | 0 0 0 0 0 0 a2 ab ac ad b2 bc bd c2 cd|
|                   |                                                         |
|                   |{-1, 4}                                                  |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|-------------------+---------------------------------------------------------|
| 0   d3 0  0  0  |)|subquotient ({4} | d  ad  0 0 -bd 0 0 0 0 -cd 0 0 0 0 0 0|
| 0   0  d3 0  0  | |             {4} | -c -ac 0 0 bc  0 0 0 0 c2  0 0 0 0 0 0|
| 0   0  0  d3 0  | |             {4} | -b -ab 0 0 b2  0 0 0 0 bc  0 0 0 0 0 0|
| cd2 0  0  0  d3 | |             {4} | a  a2  0 0 -ab 0 0 0 0 -ac 0 0 0 0 0 0|
|                   |                                                         |
|                   |{-1, 3}                                                  |
|-------------------+---------------------------------------------------------|
|                   |subquotient ({2} | 0 0 b2 bd 0 bd 0 ac ac c2 0 0 0      0|
|                   |             {3} | 0 0 -c 0  0 0  0 -d -d 0  0 0 -cd    -|
|                   |             {3} | 0 0 -a c  0 c  0 -b -b d  0 0 -bc-ad -|
|                   |             {3} | 0 0 0  -a 0 -a 0 0  0  -b 0 0 ab     a|
|                   |                                                         |
|                   |{-1, 2}                                                  |
|-------------------+---------------------------------------------------------|
|                   |subquotient (| a b c d bc-ad b3-a2c ac2-b2d c3-bd2 a2 ab |
|                   |                                                         |
|                   |{-1, 1}                                                  |
|                   |                                                         |
|                   |                                                         |
|                   |                                                         |
|-------------------+---------------------------------------------------------|
|                   |0                                                        |
|                   |                                                         |
|                   |{-1, 0}                                                  |
|-------------------+---------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
| d2 |, {5} | a2 ab ac ad b2 bc bd c2 cd d2 |)                                |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0 0 0 0 0 0 0 0 0 d  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0|
| 0 0 0 0 0 0 0 0 0 -c 0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0|
| 0 0 0 0 0 0 0 0 0 -b 0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b|
| 0 0 0 0 0 0 0 0 0 a  0  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|      0 0 0 0 0 0 0 0 0 0 0 0 0 -b2 -ac -bd -c2 a2 0  0  0  ab 0  0  0  ac 0 |
|cd    0 0 0 0 0 0 0 0 0 0 0 0 0 c   d   0   0   0  a2 0  0  0  ab 0  0  0  ac|
|bc-ad 0 0 0 0 0 0 0 0 0 0 0 0 0 a   b   -c  -d  0  0  a2 0  0  0  ab 0  0  0 |
|b     0 0 0 0 0 0 0 0 0 0 0 0 0 0   0   a   b   0  0  0  a2 0  0  0  ab 0  0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|ac ad b2 bc bd c2 cd d2 |, | bc-ad b3-a2c ac2-b2d c3-bd2 a2 ab ac ad b2 bc bd|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |, {4} | d  |
|  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |  {4} | -c |
|2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |  {4} | -b |
|  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |  {4} | a  |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0|
| 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0|
| ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0|
| 0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  c|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| c2 cd d2 |)                                                                 |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0 |
|0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd|
|0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0 |
|0  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|  d2 0  0  0  |, {2} | -b2 -ac -bd -c2 a2 0  0  0  ab 0  0  0  ac 0  0  0  ad|
|  0  d2 0  0  |  {3} | c   d   0   0   0  a2 0  0  0  ab 0  0  0  ac 0  0  0 |
|  0  0  d2 0  |  {3} | a   b   -c  -d  0  0  a2 0  0  0  ab 0  0  0  ac 0  0 |
|d 0  0  0  d2 |  {3} | 0   0   a   b   0  0  0  a2 0  0  0  ab 0  0  0  ac 0 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |)                                |
| 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |                                 |
| bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |                                 |
| 0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |                                 |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
| 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0|
| ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0|
| 0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d|
| 0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0|
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|                                                                             |
|                                                                             |
|                                                                             |
|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|-------+---------------------------------------------------------------------|
|       |0                                                                    |
|       |                                                                     |
|       |{0, 4}                                                               |
|       |                                                                     |
|       |                                                                     |
|       |                                                                     |
|-------+---------------------------------------------------------------------|
|       |subquotient ({5} | a b c d |, {5} | a b c d |)                       |
|       |                                                                     |
|       |{0, 3}                                                               |
|       |                                                                     |
|       |                                                                     |
|       |                                                                     |
|-------+---------------------------------------------------------------------|
|  0  |)|subquotient ({4} | d  d  a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 |, {4} | d  |
|  0  | |             {4} | -c -c 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 |  {4} | -c |
|2 0  | |             {4} | -b -b 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 |  {4} | -b |
|  d2 | |             {4} | a  a  0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d |  {4} | a  |
|       |                                                                     |
|       |{0, 2}                                                               |
|-------+---------------------------------------------------------------------|
|       |subquotient ({2} | ac b2 c2 bd -b2 -ac -bd -c2 a 0 0 0 b 0 0 0 c 0 0 |
|       |             {3} | -d -c 0  0  c   d   0   0   0 a 0 0 0 b 0 0 0 c 0 |
|       |             {3} | -b -a d  c  a   b   -c  -d  0 0 a 0 0 0 b 0 0 0 c |
|       |             {3} | 0  0  -b -a 0   0   a   b   0 0 0 a 0 0 0 b 0 0 0 |
|       |                                                                     |
|       |{0, 1}                                                               |
|-------+---------------------------------------------------------------------|
|       |cokernel | bc-ad b3-a2c ac2-b2d c3-bd2 a b c d |                     |
|       |                                                                     |
|       |{0, 0}                                                               |
|-------+---------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|---------------------------------------------------------------------+       |
|                                                                     |       |
|                                                                     |       |
|                                                                     |       |
|                                                                     |       |
|                                                                     |       |
|                                                                     |       |
|---------------------------------------------------------------------+       |
|                                                                     |       |
|                                                                     |       |
|                                                                     |       |
|                                                                     |       |
|                                                                     |       |
|                                                                     |       |
|---------------------------------------------------------------------+       |
|a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 |)                                   |       |
|0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 |                                    |       |
|0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 |                                    |       |
|0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d |                                    |       |
|                                                                     |       |
|                                                                     |       |
|---------------------------------------------------------------------+       |
|0 d 0 0 0 |, {2} | -b2 -ac -bd -c2 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 |)|       |
|0 0 d 0 0 |  {3} | c   d   0   0   0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 | |       |
|0 0 0 d 0 |  {3} | a   b   -c  -d  0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 | |       |
|c 0 0 0 d |  {3} | 0   0   a   b   0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d | |       |
|                                                                     |       |
|                                                                     |       |
|---------------------------------------------------------------------+       |
|                                                                     |       |
|                                                                     |       |
|                                                                     |       |
|---------------------------------------------------------------------+       |
+-----------------------------------------------------------------------------+

See also
========

  * Examples of filtered complexes and spectral sequences
    -- How to use this package

Ways to use this method:
========================

  * spectralSequencePage(FilteredComplex,ZZ)
    -- construct a spectral
    sequence page from a filtered complex
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:3278:0.

SpectralSequencePageMap -- the type of all spectral sequence page maps
**********************************************************************

Description
===========

A (homological, or lower index) spectral sequence page map consists of:

1.  A fixed integer $r \geq 0 $, the page number;

2. A collection of homomorphisms $\{d^r_{p,q}: E^r_{p,q} \rightarrow
E^r_{p-r,q+r-1}\}$ for $p,q \in \mathbb{Z}, r \geq 0$ such that $d^r_{p,q}
d^r_{p+r,q-r+1} = 0$.

Alternatively a (cohomological, or upper index) spectral sequence page consists
of:

1'.  A fixed integer $r \geq 0$, the page number;

2'.   A collection of homomorphisms $\{d_r^{p,q}: E_r^{p,q} \rightarrow
E_r^{p+r,q-r+1}\}$ for $p,q \in \mathbb{Z}, r \geq 0$ such that $d_r^{p,q}
d_r^{p-r,q+r-1} = 0$.

The type SpectralSequencePageMap is a data type for working with spectral
sequences and the differentials on the pages of a spectral sequence.

See also
========

  * SpectralSequence -- the type of all spectral
    sequences
  * SpectralSequencePage -- the type of all
    spectral sequence pages
  * PageMap -- the type of all page maps

Functions and methods returning a spectral sequence page map:
=============================================================

  * "spectralSequencePageMap(FilteredComplex,ZZ)" -- see
    spectralSequencePageMap, -- compute the maps on a
    spectral sequence page

Methods that use a spectral sequence page map:
==============================================

  * describe(SpectralSequencePageMap)
    -- real description
  * SpectralSequencePageMap ^ List, --
    the p,q th map on of a spectral sequence page
  * SpectralSequencePageMap _ List, --
    The p,q th map on of a spectral sequence page

For the programmer
==================

The object SpectralSequencePageMap, is a
type (Macaulay2Doc), with ancestor classes PageMap, <
MutableHashTable (Macaulay2Doc) < HashTable (Macaulay2Doc)
< Thing (Macaulay2Doc).

-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2422:0.

spectralSequencePageMap -- compute the maps on a spectral sequence page
***********************************************************************

  * Usage:
        d = spectralSequencePageMap(FilteredComplex, ZZ)
  * Inputs:
      * K, a filtered chain complex,
      * n, an integer (Macaulay2Doc),
  * Optional inputs (Macaulay2Doc),:
      * Prune,
        => ..., default value false,
  * Outputs:
      * D, a spectral sequence page map,

Description
===========

Returns the differentials of a spectral sequence page.

Ways to use spectralSequencePageMap:
====================================

  * "spectralSequencePageMap(FilteredComplex,ZZ)"

For the programmer
==================

The object spectralSequencePageMap, is a
method function with options (Macaulay2Doc).

-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2287:0.

SpectralSequencePageMap ^ List -- the p,q th map on of a spectral sequence page
*******************************************************************************

  * Operator: ^ (Macaulay2Doc),
  * Usage:
        d = D ^L
  * Inputs:
      * D, a spectral sequence page map,
      * L, a list (Macaulay2Doc), A list L = \{p,q\} \ of integers.
  * Outputs:
      * d, a matrix (Macaulay2Doc),

Description
===========

Returns the p,q th map on an (upper index) spectral sequence page.  The
relationship $D^{p,q} = D_{-p,-q}$ holds.

Consider the filtered complex $K$ below, obtained by multiplying the minimal
free resolution of the rational quartic space curve by successive powers of the
irrelevant ideal.

+----------------------------------------------------+
|i1 : B = QQ[a..d];                                  |
+----------------------------------------------------+
|i2 : J = ideal vars B;                              |
|                                                    |
|o2 : Ideal of B                                     |
+----------------------------------------------------+
|i3 : C = complete res monomialCurveIdeal(B,{1,3,4});|
+----------------------------------------------------+
|i4 : K = filteredComplex(J,C,4);                    |
+----------------------------------------------------+

We compute a map on the third page of the spectral sequence associated to $K$.

+-----------------------------------------------------------------------------+
|i5 : E = spectralSequence K                                                  |
|                                                                             |
|o5 = E                                                                       |
|                                                                             |
|o5 : SpectralSequence                                                        |
+-----------------------------------------------------------------------------+
|i6 : E_3 .dd^{1,-2}                                                          |
|                                                                             |
|o6 = {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 -1 0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 -1 0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  1  0  0 0 0 0 0  0  0  0 0 0 0 -1 0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  1  0  0 0 0 0 0  0  0  0 0 0 0 -1 0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 1  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  -1 0  0 0 0 0 0  0  0  0 0 0 0 1  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  -1 0 0 0 0 0  0  0  0 0 0 0 0  -1 0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  1  0 0 0 0 0  0  0  0 0 0 0 0  1  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  1  0 0 0 0 0  0  0  0 0 0 0 0  1   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  -1 0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 1  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  -1 0  0 0 0 0 0  0  0  0 0 0 0 1  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  -1 0 0 0 0 0  0  0  0 0 0 0 0  -1  |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  1  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {0} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     ------------------------------------------------------------------------|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     1  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     ------------------------------------------------------------------------|
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|                                                                             |
|o6 : Matrix                                                                  |
+-----------------------------------------------------------------------------+

See also
========

  * SpectralSequencePageMap _ List, --
    The p,q th map on of a spectral sequence page
  * Examples of filtered complexes and spectral sequences
    -- How to use this package

Ways to use this method:
========================

  * SpectralSequencePageMap ^ List, --
    the p,q th map on of a spectral sequence page
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:3440:0.

SpectralSequencePageMap _ List -- The p,q th map on of a spectral sequence page
*******************************************************************************

  * Operator: _ (Macaulay2Doc),
  * Usage:
        d = D _L
  * Inputs:
      * D, a spectral sequence page map,
      * L, a list (Macaulay2Doc), A list L = \{p,q\} \ of integers.
  * Outputs:
      * d, a matrix (Macaulay2Doc),

Description
===========

Returns the p,q th map on a (lower index) spectral sequence page.  The
relationship $D_{p,q} = D^{-p,-q}$ holds.

Consider the filtered complex $K$ below, obtained by multiplying the minimal
free resolution of the rational quartic space curve by successive powers of the
irrelevant ideal.

+----------------------------------------------------+
|i1 : B = QQ[a..d];                                  |
+----------------------------------------------------+
|i2 : J = ideal vars B;                              |
|                                                    |
|o2 : Ideal of B                                     |
+----------------------------------------------------+
|i3 : C = complete res monomialCurveIdeal(B,{1,3,4});|
+----------------------------------------------------+
|i4 : K = filteredComplex(J,C,4);                    |
+----------------------------------------------------+

We compute a map on the third page of the spectral sequence associated to $K$.

+-----------------------------------------------------------------------------+
|i5 : E = spectralSequence K                                                  |
|                                                                             |
|o5 = E                                                                       |
|                                                                             |
|o5 : SpectralSequence                                                        |
+-----------------------------------------------------------------------------+
|i6 : E^3 .dd_{-1,2}                                                          |
|                                                                             |
|o6 = {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 -1 0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 -1 0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  1  0  0 0 0 0 0  0  0  0 0 0 0 -1 0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  1  0  0 0 0 0 0  0  0  0 0 0 0 -1 0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 1  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  -1 0  0 0 0 0 0  0  0  0 0 0 0 1  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  -1 0 0 0 0 0  0  0  0 0 0 0 0  -1 0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  1  0 0 0 0 0  0  0  0 0 0 0 0  1  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  1  0 0 0 0 0  0  0  0 0 0 0 0  1   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  -1 0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 1  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  -1 0  0 0 0 0 0  0  0  0 0 0 0 1  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  -1 0 0 0 0 0  0  0  0 0 0 0 0  -1  |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  1  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {4} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {5} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     {0} | 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 0 0  0   |
|     ------------------------------------------------------------------------|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     1  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|
|     ------------------------------------------------------------------------|
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|     0 0 0 0 0 0 0 0 0 |                                                     |
|                                                                             |
|o6 : Matrix                                                                  |
+-----------------------------------------------------------------------------+

See also
========

  * SpectralSequencePageMap ^ List, --
    the p,q th map on of a spectral sequence page
  * Examples of filtered complexes and spectral sequences
    -- How to use this package

Ways to use this method:
========================

  * SpectralSequencePageMap _ List, --
    The p,q th map on of a spectral sequence page
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:3406:0.

spectralSequencePageMap(...,Prune=>...)
***************************************

Functions with optional argument named Prune:
=============================================

  * page(...,Prune=>...)
  * spectralSequence(...,Prune=>...)
  * spectralSequencePage(...,Prune=>...)
  * spectralSequencePageMap(...,Prune=>...)

Further information
===================

  * Default value: false (Macaulay2Doc),
  * Function: spectralSequencePageMap, --
    compute the maps on a spectral sequence page
  * Option key: Prune (Macaulay2Doc), -- value of an optional
    argument
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:1101:0.

spots -- which spots does the given page has a module.
******************************************************

  * Usage:
        s = spots P
  * Inputs:
      * P, a Page,
  * Outputs:
      * s, a list (Macaulay2Doc),

Description
===========

Returns a list of all the spots where the given page has a module.

Ways to use spots:
==================

  * "spots(Page)"
  * spots(ChainComplex) -- which spots does the
    given chain complex has a module.
  * spots(FilteredComplex) -- which spots
    does the given filtered complex has a module.
  * spots(PageMap)

For the programmer
==================

The object spots, is a method function (Macaulay2Doc).

-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2509:0.

spots(ChainComplex) -- which spots does the given chain complex has a module.
*****************************************************************************

  * Function: spots,
  * Usage:
        s = spots L
  * Inputs:
      * L, a chain complex (OldChainComplexes),
  * Outputs:
      * s, a list (Macaulay2Doc),

Description
===========

Returns a list of all the spots where the given chain complex has a module.

Ways to use this method:
========================

  * spots(ChainComplex) -- which spots does the
    given chain complex has a module.
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2590:0.

spots(FilteredComplex) -- which spots does the given filtered complex has a module.
***********************************************************************************

  * Function: spots,
  * Usage:
        s = spots L
  * Inputs:
      * L, a filtered chain complex,
  * Outputs:
      * s, a list (Macaulay2Doc),

Description
===========

Returns a list of all the spots where the given filtered complex has a module.

Ways to use this method:
========================

  * spots(FilteredComplex) -- which spots
    does the given filtered complex has a module.
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2638:0.

spots(PageMap)
**************

  * Function: spots,

Ways to use this method:
========================

  * spots(PageMap)
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2268:0.

support(ChainComplex) -- nonzero parts of a chain complex
*********************************************************

  * Function: support (Macaulay2Doc),

Description
===========

Computes the homological degrees in which the chain complex admits a nonzero
module

+--------------------------+
|i1 : A = QQ[x,y];         |
+--------------------------+
|i2 : C = koszul vars A    |
|                          |
|      1      2      1     |
|o2 = A  <-- A  <-- A      |
|                          |
|     0      1      2      |
|                          |
|o2 : ChainComplex         |
+--------------------------+
|i3 : support C            |
|                          |
|o3 = {0, 1, 2}            |
|                          |
|o3 : List                 |
+--------------------------+
|i4 : D = truncate(C,1)    |
|                          |
|                  2      1|
|o4 = image 0 <-- A  <-- A |
|                          |
|     0           1      2 |
|                          |
|o4 : ChainComplex         |
+--------------------------+
|i5 : spots D              |
|                          |
|o5 = {0, 1, 2}            |
|                          |
|o5 : List                 |
+--------------------------+
|i6 : support D            |
|                          |
|o6 = {1, 2}               |
|                          |
|o6 : List                 |
+--------------------------+

See also
========

  * spots(ChainComplex) -- which spots does the
    given chain complex has a module.

Ways to use this method:
========================

  * support(ChainComplex) -- nonzero parts of
    a chain complex
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2821:0.

support(FilteredComplex)
************************

  * Function: support (Macaulay2Doc),

Ways to use this method:
========================

  * support(FilteredComplex)
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2244:0.

support(Page) -- which non-zero modules appear in the given page.
*****************************************************************

  * Function: support (Macaulay2Doc),
  * Usage:
        l = support P
  * Inputs:
      * P, a Page,
  * Outputs:
      * l, a list (Macaulay2Doc),

Description
===========

Returns a list of all the non-zero modules appearing in the given page has a
module.

Ways to use this method:
========================

  * support(Page) -- which non-zero modules appear in
    the given page.
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2528:0.

support(PageMap)
****************

  * Function: support (Macaulay2Doc),

Ways to use this method:
========================

  * support(PageMap)
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2256:0.

support(SpectralSequencePage)
*****************************

  * Function: support (Macaulay2Doc),

Ways to use this method:
========================

  * support(SpectralSequencePage)
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2262:0.

targetPruningMap
****************

For the programmer
==================

The object targetPruningMap, is a symbol (Macaulay2Doc).

-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:1061:0.

tensor(RingMap,ChainComplex) -- tensor product of a chain complex by a ring map
*******************************************************************************

  * Function: tensor (Macaulay2Doc),
  * Usage:
        D = tensor(f,C)
  * Inputs:
      * f, a ring map (Macaulay2Doc),
      * C, a chain complex (OldChainComplexes),
  * Outputs:
      * D, a chain complex (OldChainComplexes),

Description
===========

Given a ring map R -> S and a chain complex over R, returns the tensor product
of the given chain complex.

+----------------------+
|i1 : R = QQ[x];       |
+----------------------+
|i2 : M = R^1/(x^2);   |
+----------------------+
|i3 : S = R/(x^4);     |
+----------------------+
|i4 : C = res M        |
|                      |
|      1      1        |
|o4 = R  <-- R  <-- 0  |
|                      |
|     0      1      2  |
|                      |
|o4 : ChainComplex     |
+----------------------+
|i5 : f = map(S,R,{1});|
|                      |
|o5 : RingMap S <-- R  |
+----------------------+
|i6 : tensor(f,C)      |
|                      |
|      1      1        |
|o6 = S  <-- S  <-- 0  |
|                      |
|     0      1      2  |
|                      |
|o6 : ChainComplex     |
+----------------------+

See also
========

  * Filtrations and tensor product complexes

Ways to use this method:
========================

  * tensor(RingMap,ChainComplex), --
    tensor product of a chain complex by a ring map
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:3614:0.

The fibration of the Klein Bottle over the sphere with fibers the sphere
************************************************************************

In this example we give a simplicial realization of the fibration $\mathbb{S}^1
\rightarrow {\rm Klein Bottle} \rightarrow \mathbb{S}^1$. To give a simplicial
realization of this fibration we first make a simplicial complex which gives a
triangulation of the Klein Bottle. The triangulation of the Klein Bottle that
we use has 18 facets and is, up to relabling, the triangulation of the Klein
bottle given in Figure 6.14 of Armstrong's book Basic Topology.

+-----------------------------------------------------------------------------+
|i1 : S = ZZ[a00,a10,a20,a01,a11,a21,a02,a12,a22];                            |
+-----------------------------------------------------------------------------+
|i2 : Delta = simplicialComplex {a00*a10*a02,                                 |
|                                                                             |
|o2 = simplicialComplex | a11a12a22 a20a12a22                                 |
|                                                                             |
|o2 : SimplicialComplex                                                       |
|-----------------------------------------------------------------------------|
|a02*a12*a10, a01*a02*a12, a01*a12*a11, a00*a01*a11, a00*a11*a10, a10*        |
|                                                                             |
|a11a21a22 a01a21a22 a00a01a22 a00a20a22 a01a02a12 a10a02a12 a01a11a12        |
|-----------------------------------------------------------------------------|
|a12*a20, a12*a20*a22, a11*a12*a22, a11*a22*a21, a10*a11*a21,                 |
|                                                                             |
| a10a20a12 a01a21a02 a20a21a02 a00a20a02 a00a10a02 a10a11a21                 |
|-----------------------------------------------------------------------------|
|a10*a21*a20, a20*a22*a00, a22*a00*a01, a21*a22*a01, a21*a02*a01, a20*a21*a02,|
|                                                                             |
|a10a20a21 a00a01a11 a00a10a11 |                                              |
|-----------------------------------------------------------------------------|
|a20*a02*a00}                                                                 |
+-----------------------------------------------------------------------------+

We can check that the homology of this simplicial complex agrees with that of
the Klein Bottle:

+-----------------------------------------------+
|i3 : C = truncate(chainComplex complex Delta,1)|
|                                               |
|                   9       27       18         |
|o3 = image 0 <-- ZZ  <-- ZZ   <-- ZZ           |
|                                               |
|     -1          0       1        2            |
|                                               |
|o3 : ChainComplex                              |
+-----------------------------------------------+
|i4 : prune HH C                                |
|                                               |
|o4 = -1 : 0                                    |
|                                               |
|            1                                  |
|      0 : ZZ                                   |
|                                               |
|      1 : cokernel | 2 |                       |
|                   | 0 |                       |
|                                               |
|      2 : 0                                    |
|                                               |
|o4 : GradedModule                              |
+-----------------------------------------------+

Let $S$ be the simplicial complex with facets $\{A_0 A_1, A_0 A_2, A_1 A_2\}$.
Then $S$ is a triangulation of $S^1$.  The simplicial map $\pi : \Delta
\rightarrow S$ given by $\pi(a_{i,j}) = A_i$ is a combinatorial realization of
the fibration $S^1 \rightarrow {\rm Klein Bottle} \rightarrow S^1$. The
subsimplicial complexes of $\Delta$, which arise from the the inverse images of
the simplicies of $S$, are described below.

+-----------------------------------------------------------------------------+
|i5 : F1Delta = Delta                                                         |
|                                                                             |
|o5 = simplicialComplex | a11a12a22 a20a12a22 a11a21a22 a01a21a22 a00a01a22   |
|                                                                             |
|o5 : SimplicialComplex                                                       |
|-----------------------------------------------------------------------------|
|a00a20a22 a01a02a12 a10a02a12 a01a11a12 a10a20a12 a01a21a02 a20a21a02        |
|-----------------------------------------------------------------------------|
|a00a20a02 a00a10a02 a10a11a21 a10a20a21 a00a01a11 a00a10a11 |                |
+-----------------------------------------------------------------------------+
|i6 : F0Delta = simplicialComplex {a00*a01,a01*a02,a00*a02,a10*a11,a10*a12,   |
|                                                                             |
|o6 = simplicialComplex | a21a22 a20a22 a11a12 a10a12 a01a02 a00a02 a20a21    |
|                                                                             |
|o6 : SimplicialComplex                                                       |
|-----------------------------------------------------------------------------|
|a11*a12,a21*a20,a20*a22,a21*a22}                                             |
|                                                                             |
|a10a11 a00a01 |                                                              |
+-----------------------------------------------------------------------------+

The resulting filtered chain complex is:

+-----------------------------------------------------------------------------+
|i7 : K = filteredComplex({F1Delta, F0Delta}, ReducedHomology => false)       |
|                                                                             |
|o7 = -1 : image 0 <-- image 0 <-- image 0 <-- image 0                        |
|                                                                             |
|          -1          0           1           2                              |
|                                                                             |
|     0 : image 0 <-- image | 1 0 0 0 0 0 0 0 0 | <-- image | 0 0 0 0 0 0 0 0 |
|                           | 0 1 0 0 0 0 0 0 0 |           | 0 0 0 0 0 0 0 0 |
|         -1                | 0 0 1 0 0 0 0 0 0 |           | 1 0 0 0 0 0 0 0 |
|                           | 0 0 0 1 0 0 0 0 0 |           | 0 0 0 0 0 0 0 0 |
|                           | 0 0 0 0 1 0 0 0 0 |           | 0 1 0 0 0 0 0 0 |
|                           | 0 0 0 0 0 1 0 0 0 |           | 0 0 0 0 0 0 0 0 |
|                           | 0 0 0 0 0 0 1 0 0 |           | 0 0 0 0 0 0 0 0 |
|                           | 0 0 0 0 0 0 0 1 0 |           | 0 0 1 0 0 0 0 0 |
|                           | 0 0 0 0 0 0 0 0 1 |           | 0 0 0 0 0 0 0 0 |
|                                                           | 0 0 0 0 0 0 0 0 |
|                     0                                     | 0 0 0 1 0 0 0 0 |
|                                                           | 0 0 0 0 1 0 0 0 |
|                                                           | 0 0 0 0 0 0 0 0 |
|                                                           | 0 0 0 0 0 0 0 0 |
|                                                           | 0 0 0 0 0 1 0 0 |
|                                                           | 0 0 0 0 0 0 0 0 |
|                                                           | 0 0 0 0 0 0 0 0 |
|                                                           | 0 0 0 0 0 0 1 0 |
|                                                           | 0 0 0 0 0 0 0 0 |
|                                                           | 0 0 0 0 0 0 0 0 |
|                                                           | 0 0 0 0 0 0 0 0 |
|                                                           | 0 0 0 0 0 0 0 1 |
|                                                           | 0 0 0 0 0 0 0 0 |
|                                                           | 0 0 0 0 0 0 0 0 |
|                                                           | 0 0 0 0 0 0 0 0 |
|                                                           | 0 0 0 0 0 0 0 0 |
|                                                           | 0 0 0 0 0 0 0 0 |
|                                                                             |
|                                                     1                       |
|                                                                             |
|                       9       27       18                                   |
|     1 : image 0 <-- ZZ  <-- ZZ   <-- ZZ                                     |
|                                                                             |
|         -1          0       1        2                                      |
|                                                                             |
|o7 : FilteredComplex                                                         |
|-----------------------------------------------------------------------------|
|0 | <-- image 0                                                              |
|0 |                                                                          |
|0 |     2                                                                    |
|0 |                                                                          |
|0 |                                                                          |
|0 |                                                                          |
|0 |                                                                          |
|0 |                                                                          |
|0 |                                                                          |
|0 |                                                                          |
|0 |                                                                          |
|0 |                                                                          |
|0 |                                                                          |
|0 |                                                                          |
|0 |                                                                          |
|0 |                                                                          |
|0 |                                                                          |
|0 |                                                                          |
|0 |                                                                          |
|0 |                                                                          |
|0 |                                                                          |
|0 |                                                                          |
|0 |                                                                          |
|0 |                                                                          |
|1 |                                                                          |
|0 |                                                                          |
|0 |                                                                          |
+-----------------------------------------------------------------------------+

The resulting spectral sequence is:

+-----------------------------------------------------------------------------+
|i8 : E = prune spectralSequence K                                            |
|                                                                             |
|o8 = E                                                                       |
|                                                                             |
|o8 : SpectralSequence                                                        |
+-----------------------------------------------------------------------------+
|i9 : E^0                                                                     |
|                                                                             |
|     +------+------+                                                         |
|     |  9   |  18  |                                                         |
|o9 = |ZZ    |ZZ    |                                                         |
|     |      |      |                                                         |
|     |{0, 1}|{1, 1}|                                                         |
|     +------+------+                                                         |
|     |  9   |  18  |                                                         |
|     |ZZ    |ZZ    |                                                         |
|     |      |      |                                                         |
|     |{0, 0}|{1, 0}|                                                         |
|     +------+------+                                                         |
|                                                                             |
|o9 : SpectralSequencePage                                                    |
+-----------------------------------------------------------------------------+
|i10 : E^0 .dd                                                                |
|                                                                             |
|o10 = {-1, 0} : 0 <----- 0 : {-1, 1}                                         |
|                     0                                                       |
|                                                                             |
|      {-1, 1} : 0 <----- 0 : {-1, 2}                                         |
|                     0                                                       |
|                                                                             |
|      {-1, 2} : 0 <----- 0 : {-1, 3}                                         |
|                     0                                                       |
|                                                                             |
|      {1, -3} : 0 <----- 0 : {1, -2}                                         |
|                     0                                                       |
|                                                                             |
|      {1, -2} : 0 <----- 0 : {1, -1}                                         |
|                     0                                                       |
|                                                                             |
|                           18                                                |
|      {1, -1} : 0 <----- ZZ   : {1, 0}                                       |
|                     0                                                       |
|                                                                             |
|                 18                                                          |
|      {1, 0} : ZZ   <--------------------------------------------------------|
|                       | -1 -1 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  -1 -1 0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 1  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  1  0  1  0  0  0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  -1 -1 0  0  0  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  1  0  1  0  0  0  0  0  0  0  0  0|
|                       | 0  -1 0  0  0  0  0  0  0  -1 0  0  0  0  0  0  0  0|
|                       | 0  0  -1 0  0  0  0  0  0  0  1  0  0  0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  -1 0  0  0  -1 0  0  0  0  0  0|
|                       | 0  0  0  0  -1 0  0  0  0  0  0  0  -1 0  0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  -1 -1 0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  1  0  0  1  0  0|
|                       | 0  0  0  0  0  -1 0  0  0  0  0  0  0  0  1  0  0  0|
|                       | 0  0  0  0  0  0  0  0  -1 0  0  0  0  0  0  0  -1 0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  1|
|                       | 0  0  0  0  0  0  0  0  0  0  -1 0  0  -1 0  0  0  0|
|                       | 0  0  0  0  0  0  0  0  0  -1 0  0  0  0  0  -1 0  0|
|                       | 0  0  0  0  0  0  0  0  0  0  0  -1 0  0  0  0  0  -|
|                                                                             |
|      {0, -2} : 0 <----- 0 : {0, -1}                                         |
|                     0                                                       |
|                                                                             |
|                           9                                                 |
|      {0, -1} : 0 <----- ZZ  : {0, 0}                                        |
|                     0                                                       |
|                                                                             |
|                 9                                       9                   |
|      {0, 0} : ZZ  <---------------------------------- ZZ  : {0, 1}          |
|                      | 1  1  0  0  0  0  0  0  0  |                         |
|                      | 0  0  1  1  0  0  0  0  0  |                         |
|                      | 0  0  0  0  1  1  0  0  0  |                         |
|                      | -1 0  0  0  0  0  1  0  0  |                         |
|                      | 0  0  -1 0  0  0  0  1  0  |                         |
|                      | 0  0  0  0  -1 0  0  0  1  |                         |
|                      | 0  -1 0  0  0  0  -1 0  0  |                         |
|                      | 0  0  0  -1 0  0  0  -1 0  |                         |
|                      | 0  0  0  0  0  -1 0  0  -1 |                         |
|                                                                             |
|                 9                                                           |
|      {0, 1} : ZZ  <----- 0 : {0, 2}                                         |
|                      0                                                      |
|                                                                             |
|      {-1, -1} : 0 <----- 0 : {-1, 0}                                        |
|                      0                                                      |
|                                                                             |
|o10 : SpectralSequencePageMap                                                |
|-----------------------------------------------------------------------------|
|        18                                                                   |
|----- ZZ   : {1, 1}                                                          |
|  |                                                                          |
|  |                                                                          |
|  |                                                                          |
|  |                                                                          |
|  |                                                                          |
|  |                                                                          |
|  |                                                                          |
|  |                                                                          |
|  |                                                                          |
|  |                                                                          |
|  |                                                                          |
|  |                                                                          |
|  |                                                                          |
|  |                                                                          |
|  |                                                                          |
|  |                                                                          |
|  |                                                                          |
|1 |                                                                          |
+-----------------------------------------------------------------------------+
|i11 : E^1                                                                    |
|                                                                             |
|      +------+------+                                                        |
|      |  3   |  3   |                                                        |
|o11 = |ZZ    |ZZ    |                                                        |
|      |      |      |                                                        |
|      |{0, 1}|{1, 1}|                                                        |
|      +------+------+                                                        |
|      |  3   |  3   |                                                        |
|      |ZZ    |ZZ    |                                                        |
|      |      |      |                                                        |
|      |{0, 0}|{1, 0}|                                                        |
|      +------+------+                                                        |
|                                                                             |
|o11 : SpectralSequencePage                                                   |
+-----------------------------------------------------------------------------+
|i12 : E^1 .dd                                                                |
|                                                                             |
|o12 = {-2, 1} : 0 <----- 0 : {-1, 1}                                         |
|                     0                                                       |
|                                                                             |
|      {-2, 2} : 0 <----- 0 : {-1, 2}                                         |
|                     0                                                       |
|                                                                             |
|      {-2, 3} : 0 <----- 0 : {-1, 3}                                         |
|                     0                                                       |
|                                                                             |
|      {0, -2} : 0 <----- 0 : {1, -2}                                         |
|                     0                                                       |
|                                                                             |
|      {0, -1} : 0 <----- 0 : {1, -1}                                         |
|                     0                                                       |
|                                                                             |
|                 3                     3                                     |
|      {0, 0} : ZZ  <---------------- ZZ  : {1, 0}                            |
|                      | -1 1  0  |                                           |
|                      | 0  -1 1  |                                           |
|                      | 1  0  -1 |                                           |
|                                                                             |
|                 3                    3                                      |
|      {0, 1} : ZZ  <--------------- ZZ  : {1, 1}                             |
|                      | 1 1  0  |                                            |
|                      | 0 -1 1  |                                            |
|                      | 1 0  -1 |                                            |
|                                                                             |
|      {-1, -1} : 0 <----- 0 : {0, -1}                                        |
|                      0                                                      |
|                                                                             |
|                           3                                                 |
|      {-1, 0} : 0 <----- ZZ  : {0, 0}                                        |
|                     0                                                       |
|                                                                             |
|                           3                                                 |
|      {-1, 1} : 0 <----- ZZ  : {0, 1}                                        |
|                     0                                                       |
|                                                                             |
|      {-1, 2} : 0 <----- 0 : {0, 2}                                          |
|                     0                                                       |
|                                                                             |
|      {-2, 0} : 0 <----- 0 : {-1, 0}                                         |
|                     0                                                       |
|                                                                             |
|o12 : SpectralSequencePageMap                                                |
+-----------------------------------------------------------------------------+
|i13 : E^2                                                                    |
|                                                                             |
|      +--------------+------+                                                |
|o13 = |cokernel | 2 ||0     |                                                |
|      |              |      |                                                |
|      |{0, 1}        |{1, 1}|                                                |
|      +--------------+------+                                                |
|      |  1           |  1   |                                                |
|      |ZZ            |ZZ    |                                                |
|      |              |      |                                                |
|      |{0, 0}        |{1, 0}|                                                |
|      +--------------+------+                                                |
|                                                                             |
|o13 : SpectralSequencePage                                                   |
+-----------------------------------------------------------------------------+

Note that the spectral sequence is abutting to what it should — the integral
homology of the Klein bottle

-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:1664:0.

The trivial fibration over the sphere with fibers the sphere
************************************************************

In this example we compute the spectral sequence associated to the trivial
fibration $\mathbb{S}^1 \rightarrow  \mathbb{S}^1 x \mathbb{S}^1 \rightarrow
\mathbb{S}^1$, where the map is given by one of the projections.  To give a
simplicial realization of this fibration we first make a simplicial complex
which gives a triangulation of $\mathbb{S}^1 \times \mathbb{S}^1$.  The
simplicial complex that we construct is the triangulation of the torus given in
Figure 6.4 of Armstrong's book Basic Topology and has 18 facets.

+-----------------------------------------------------------------------------+
|i1 : S = ZZ/101[a00,a10,a20,a01,a11,a21,a02,a12,a22];                        |
+-----------------------------------------------------------------------------+
|i2 : Delta = simplicialComplex {a00*a02*a10,                                 |
|                                                                             |
|o2 = simplicialComplex | a11a12a22 a20a12a22                                 |
|                                                                             |
|o2 : SimplicialComplex                                                       |
|-----------------------------------------------------------------------------|
|a02*a12*a10, a01*a02*a12, a01*a11*a12, a00*a01*a11, a00*a10*a11, a12*        |
|                                                                             |
|a21a02a22 a00a02a22 a11a21a22 a00a20a22 a01a02a12 a10a02a12 a01a11a12        |
|-----------------------------------------------------------------------------|
|a10*a20, a12*a20*a22, a11*a12*a22, a11*a22*a21, a10*a11*a21,                 |
|                                                                             |
| a10a20a12 a01a21a02 a00a10a02 a10a11a21 a20a01a21 a10a20a21                 |
|-----------------------------------------------------------------------------|
|a10*a21*a20, a20*a22*a00, a22*a00*a02, a21*a22*a02, a21*a02*a01, a20*a21*a01,|
|                                                                             |
|a00a01a11 a00a10a11 a00a20a01 |                                              |
|-----------------------------------------------------------------------------|
|a20*a01*a00}                                                                 |
+-----------------------------------------------------------------------------+

We can check that the homology of the simplicial complex $\Delta$ agrees with
that of the torus $\mathbb{S}^1 \times \mathbb{S}^1 $

+-----------------------------------------------+
|i3 : C = truncate(chainComplex complex Delta,1)|
|                                               |
|                   ZZ 9       ZZ 27       ZZ 18|
|o3 = image 0 <-- (---)  <-- (---)   <-- (---)  |
|                  101        101         101   |
|     -1                                        |
|                 0          1           2      |
|                                               |
|o3 : ChainComplex                              |
+-----------------------------------------------+
|i4 : prune HH C                                |
|                                               |
|o4 = -1 : 0                                    |
|                                               |
|            ZZ 1                               |
|      0 : (---)                                |
|           101                                 |
|                                               |
|            ZZ 2                               |
|      1 : (---)                                |
|           101                                 |
|                                               |
|            ZZ 1                               |
|      2 : (---)                                |
|           101                                 |
|                                               |
|o4 : GradedModule                              |
+-----------------------------------------------+

Let $S$ be the simplicial complex with facets $\{A_0 A_1, A_0 A_2, A_1 A_2\}$.
Then $S$ is a triangulation of $S^1$.  The simplicial map $\pi : \Delta
\rightarrow S$ given by $\pi(a_{i,j}) = A_i$ is a combinatorial realization of
the trivial fibration $\mathbb{S}^1 \rightarrow \mathbb{S}^1 \times
\mathbb{S}^1 \rightarrow \mathbb{S}^1$. We now make subsimplicial complexes
arising from the filtrations of the inverse images of the simplicies.

+-----------------------------------------------------------------------------+
|i5 : F1Delta = Delta;                                                        |
+-----------------------------------------------------------------------------+
|i6 : F0Delta = simplicialComplex {a00*a01, a01*a02, a00*a02,                 |
|-----------------------------------------------------------------------------|
|a10*a11,a11*a12,a10*a12, a21*a20,a21*a22,a20*a22};                           |
+-----------------------------------------------------------------------------+
|i7 : K = filteredComplex({F1Delta, F0Delta}, ReducedHomology => false) ;     |
+-----------------------------------------------------------------------------+

The resulting spectral sequence is:

+-----------------------------------------------------------------------------+
|i8 : E = prune spectralSequence K                                            |
|                                                                             |
|o8 = E                                                                       |
|                                                                             |
|o8 : SpectralSequence                                                        |
+-----------------------------------------------------------------------------+
|i9 : E^0                                                                     |
|                                                                             |
|     +------+-------+                                                        |
|     |  ZZ 9|  ZZ 18|                                                        |
|o9 = |(---) |(---)  |                                                        |
|     | 101  | 101   |                                                        |
|     |      |       |                                                        |
|     |{0, 1}|{1, 1} |                                                        |
|     +------+-------+                                                        |
|     |  ZZ 9|  ZZ 18|                                                        |
|     |(---) |(---)  |                                                        |
|     | 101  | 101   |                                                        |
|     |      |       |                                                        |
|     |{0, 0}|{1, 0} |                                                        |
|     +------+-------+                                                        |
|                                                                             |
|o9 : SpectralSequencePage                                                    |
+-----------------------------------------------------------------------------+
|i10 : E^0 .dd                                                                |
|                                                                             |
|o10 = {-1, 0} : 0 <----- 0 : {-1, 1}                                         |
|                     0                                                       |
|                                                                             |
|      {-1, 1} : 0 <----- 0 : {-1, 2}                                         |
|                     0                                                       |
|                                                                             |
|      {-1, 2} : 0 <----- 0 : {-1, 3}                                         |
|                     0                                                       |
|                                                                             |
|      {1, -3} : 0 <----- 0 : {1, -2}                                         |
|                     0                                                       |
|                                                                             |
|      {1, -2} : 0 <----- 0 : {1, -1}                                         |
|                     0                                                       |
|                                                                             |
|                           ZZ 18                                             |
|      {1, -1} : 0 <----- (---)   : {1, 0}                                    |
|                     0    101                                                |
|                                                                             |
|                 ZZ 18                                                       |
|      {1, 0} : (---)   <-----------------------------------------------------|
|                101       | -1 -1 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0|
|                          | 0  0  -1 -1 0  0  0  0  0  0  0  0  0  0  0  0  0|
|                          | 1  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0|
|                          | 0  0  0  1  0  1  0  0  0  0  0  0  0  0  0  0  0|
|                          | 0  0  0  0  0  0  -1 -1 0  0  0  0  0  0  0  0  0|
|                          | 0  0  0  0  0  0  1  0  1  0  0  0  0  0  0  0  0|
|                          | 0  -1 0  0  0  0  0  0  0  -1 0  0  0  0  0  0  0|
|                          | 0  0  -1 0  0  0  0  0  0  0  -1 0  0  0  0  0  0|
|                          | 0  0  0  0  0  0  0  -1 0  0  0  -1 0  0  0  0  0|
|                          | 0  0  0  0  -1 0  0  0  0  0  0  0  -1 0  0  0  0|
|                          | 0  0  0  0  0  0  0  0  0  0  -1 0  0  -1 0  0  0|
|                          | 0  0  0  0  0  0  0  0  0  0  0  0  1  0  1  0  0|
|                          | 0  0  0  0  0  0  0  0  -1 0  0  0  0  0  0  -1 0|
|                          | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  1|
|                          | 0  0  0  0  0  0  0  0  0  0  0  0  0  -1 0  0  0|
|                          | 0  0  0  0  0  0  0  0  0  -1 0  0  0  0  -1 0  0|
|                          | 0  0  0  0  0  -1 0  0  0  0  0  0  0  0  0  0  0|
|                          | 0  0  0  0  0  0  0  0  0  0  0  -1 0  0  0  0  -|
|                                                                             |
|      {0, -2} : 0 <----- 0 : {0, -1}                                         |
|                     0                                                       |
|                                                                             |
|                           ZZ 9                                              |
|      {0, -1} : 0 <----- (---)  : {0, 0}                                     |
|                     0    101                                                |
|                                                                             |
|                 ZZ 9                                       ZZ 9             |
|      {0, 0} : (---)  <---------------------------------- (---)  : {0, 1}    |
|                101      | 1  1  0  0  0  0  0  0  0  |    101               |
|                         | 0  0  1  1  0  0  0  0  0  |                      |
|                         | 0  0  0  0  1  1  0  0  0  |                      |
|                         | -1 0  0  0  0  0  1  0  0  |                      |
|                         | 0  0  -1 0  0  0  0  1  0  |                      |
|                         | 0  0  0  0  -1 0  0  0  1  |                      |
|                         | 0  -1 0  0  0  0  -1 0  0  |                      |
|                         | 0  0  0  -1 0  0  0  -1 0  |                      |
|                         | 0  0  0  0  0  -1 0  0  -1 |                      |
|                                                                             |
|                 ZZ 9                                                        |
|      {0, 1} : (---)  <----- 0 : {0, 2}                                      |
|                101      0                                                   |
|                                                                             |
|      {-1, -1} : 0 <----- 0 : {-1, 0}                                        |
|                      0                                                      |
|                                                                             |
|o10 : SpectralSequencePageMap                                                |
|-----------------------------------------------------------------------------|
|           ZZ 18                                                             |
|-------- (---)   : {1, 1}                                                    |
|  0  |    101                                                                |
|  0  |                                                                       |
|  0  |                                                                       |
|  0  |                                                                       |
|  0  |                                                                       |
|  0  |                                                                       |
|  0  |                                                                       |
|  0  |                                                                       |
|  0  |                                                                       |
|  0  |                                                                       |
|  0  |                                                                       |
|  0  |                                                                       |
|  0  |                                                                       |
|  0  |                                                                       |
|  -1 |                                                                       |
|  0  |                                                                       |
|  -1 |                                                                       |
|1 0  |                                                                       |
+-----------------------------------------------------------------------------+
|i11 : E^1                                                                    |
|                                                                             |
|      +------+------+                                                        |
|      |  ZZ 3|  ZZ 3|                                                        |
|o11 = |(---) |(---) |                                                        |
|      | 101  | 101  |                                                        |
|      |      |      |                                                        |
|      |{0, 1}|{1, 1}|                                                        |
|      +------+------+                                                        |
|      |  ZZ 3|  ZZ 3|                                                        |
|      |(---) |(---) |                                                        |
|      | 101  | 101  |                                                        |
|      |      |      |                                                        |
|      |{0, 0}|{1, 0}|                                                        |
|      +------+------+                                                        |
|                                                                             |
|o11 : SpectralSequencePage                                                   |
+-----------------------------------------------------------------------------+
|i12 : E^1 .dd                                                                |
|                                                                             |
|o12 = {-2, 1} : 0 <----- 0 : {-1, 1}                                         |
|                     0                                                       |
|                                                                             |
|      {-2, 2} : 0 <----- 0 : {-1, 2}                                         |
|                     0                                                       |
|                                                                             |
|      {-2, 3} : 0 <----- 0 : {-1, 3}                                         |
|                     0                                                       |
|                                                                             |
|      {0, -2} : 0 <----- 0 : {1, -2}                                         |
|                     0                                                       |
|                                                                             |
|      {0, -1} : 0 <----- 0 : {1, -1}                                         |
|                     0                                                       |
|                                                                             |
|                 ZZ 3                     ZZ 3                               |
|      {0, 0} : (---)  <---------------- (---)  : {1, 0}                      |
|                101      | 1  1  0  |    101                                 |
|                         | -1 0  1  |                                        |
|                         | 0  -1 -1 |                                        |
|                                                                             |
|                 ZZ 3                     ZZ 3                               |
|      {0, 1} : (---)  <---------------- (---)  : {1, 1}                      |
|                101      | -1 0  -1 |    101                                 |
|                         | 1  -1 0  |                                        |
|                         | 0  1  1  |                                        |
|                                                                             |
|      {-1, -1} : 0 <----- 0 : {0, -1}                                        |
|                      0                                                      |
|                                                                             |
|                           ZZ 3                                              |
|      {-1, 0} : 0 <----- (---)  : {0, 0}                                     |
|                     0    101                                                |
|                                                                             |
|                           ZZ 3                                              |
|      {-1, 1} : 0 <----- (---)  : {0, 1}                                     |
|                     0    101                                                |
|                                                                             |
|      {-1, 2} : 0 <----- 0 : {0, 2}                                          |
|                     0                                                       |
|                                                                             |
|      {-2, 0} : 0 <----- 0 : {-1, 0}                                         |
|                     0                                                       |
|                                                                             |
|o12 : SpectralSequencePageMap                                                |
+-----------------------------------------------------------------------------+
|i13 : E^2                                                                    |
|                                                                             |
|      +------+------+                                                        |
|      |  ZZ 1|  ZZ 1|                                                        |
|o13 = |(---) |(---) |                                                        |
|      | 101  | 101  |                                                        |
|      |      |      |                                                        |
|      |{0, 1}|{1, 1}|                                                        |
|      +------+------+                                                        |
|      |  ZZ 1|  ZZ 1|                                                        |
|      |(---) |(---) |                                                        |
|      | 101  | 101  |                                                        |
|      |      |      |                                                        |
|      |{0, 0}|{1, 0}|                                                        |
|      +------+------+                                                        |
|                                                                             |
|o13 : SpectralSequencePage                                                   |
+-----------------------------------------------------------------------------+
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:1709:0.

truncate(ChainComplex,ZZ) -- compute the hard truncation of a chain complex
***************************************************************************

  * Function: truncate (Macaulay2Doc),

Description
===========

Computes the hard truncation of a chain complex as a specified homological
degree.

+------------------------------------------------------------+
|i1 : B = QQ[a..d];                                          |
+------------------------------------------------------------+
|i2 : C = koszul vars B                                      |
|                                                            |
|      1      4      6      4      1                         |
|o2 = B  <-- B  <-- B  <-- B  <-- B                          |
|                                                            |
|     0      1      2      3      4                          |
|                                                            |
|o2 : ChainComplex                                           |
+------------------------------------------------------------+
|i3 : truncate(C,1)                                          |
|                                                            |
|                  4      6      4      1                    |
|o3 = image 0 <-- B  <-- B  <-- B  <-- B                     |
|                                                            |
|     0           1      2      3      4                     |
|                                                            |
|o3 : ChainComplex                                           |
+------------------------------------------------------------+
|i4 : truncate(C,-1)                                         |
|                                                            |
|      1      4      6      4                                |
|o4 = B  <-- B  <-- B  <-- B  <-- image 0                    |
|                                                            |
|     0      1      2      3      4                          |
|                                                            |
|o4 : ChainComplex                                           |
+------------------------------------------------------------+
|i5 : truncate(C,-10)                                        |
|                                                            |
|o5 = image 0 <-- image 0 <-- image 0 <-- image 0 <-- image 0|
|                                                            |
|     0           1           2           3           4      |
|                                                            |
|o5 : ChainComplex                                           |
+------------------------------------------------------------+
|i6 : truncate(C,10)                                         |
|                                                            |
|o6 = image 0 <-- image 0 <-- image 0 <-- image 0 <-- image 0|
|                                                            |
|     0           1           2           3           4      |
|                                                            |
|o6 : ChainComplex                                           |
+------------------------------------------------------------+

Ways to use this method:
========================

  * truncate(ChainComplex,ZZ), --
    compute the hard truncation of a chain complex
-------------------------------------------------------------------------------

The source of this document is in SpectralSequences.m2:2767:0.